{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "u3Zq5VrfiDqB"
      },
      "source": [
        "##### Copyright 2021 The TensorFlow Authors.\n",
        "\n",
        "Licensed under the Apache License, Version 2.0 (the \"License\");"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "cellView": "form",
        "id": "3jTEqPzFiHQ0"
      },
      "outputs": [],
      "source": [
        "#@title Licensed under the Apache License, Version 2.0 (the \"License\"); { display-mode: \"form\" }\n",
        "# you may not use this file except in compliance with the License.\n",
        "# You may obtain a copy of the License at\n",
        "#\n",
        "# https://www.apache.org/licenses/LICENSE-2.0\n",
        "#\n",
        "# Unless required by applicable law or agreed to in writing, software\n",
        "# distributed under the License is distributed on an \"AS IS\" BASIS,\n",
        "# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
        "# See the License for the specific language governing permissions and\n",
        "# limitations under the License."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "x97n3SaNmNpB"
      },
      "source": [
        "# Variational Inference on Probabilistic Graphical Models with Joint Distributions\n",
        "\n",
        "<table class=\"tfo-notebook-buttons\" align=\"left\">\n",
        "  <td>\n",
        "    <a target=\"_blank\" href=\"https://www.tensorflow.org/probability/examples/Variational_Inference_and_Joint_Distributions\"><img src=\"https://www.tensorflow.org/images/tf_logo_32px.png\" />View on TensorFlow.org</a>\n",
        "  </td>\n",
        "  <td>\n",
        "    <a target=\"_blank\" href=\"https://colab.research.google.com/github/tensorflow/probability/blob/main/tensorflow_probability/examples/jupyter_notebooks/Variational_Inference_and_Joint_Distributions.ipynb\"><img src=\"https://www.tensorflow.org/images/colab_logo_32px.png\" />Run in Google Colab</a>\n",
        "  </td>\n",
        "  <td>\n",
        "    <a target=\"_blank\" href=\"https://github.com/tensorflow/probability/blob/main/tensorflow_probability/examples/jupyter_notebooks/Variational_Inference_and_Joint_Distributions.ipynb\"><img src=\"https://www.tensorflow.org/images/GitHub-Mark-32px.png\" />View source on GitHub</a>\n",
        "  </td>\n",
        "  <td>\n",
        "    <a href=\"https://storage.googleapis.com/tensorflow_docs/probability/examples/jupyter_notebooks/Variational_Inference_and_Joint_Distributions.ipynb\"><img src=\"https://www.tensorflow.org/images/download_logo_32px.png\" />Download notebook</a>\n",
        "  </td>\n",
        "</table>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SVcOch4u2bVS"
      },
      "source": [
        "Variational Inference (VI) casts approximate Bayesian inference as an optimization problem and seeks a 'surrogate' posterior distribution that minimizes the KL divergence with the true posterior. Gradient-based VI is often faster than MCMC methods, composes naturally with optimization of model parameters, and provides a lower bound on model evidence that can be used directly for model comparison, convergence diagnosis, and composable inference.\n",
        "\n",
        "TensorFlow Probability offers tools for fast, flexible, and scalable VI that fit naturally into the TFP stack. These tools enable the construction of surrogate posteriors with covariance structures induced by linear transformations or normalizing flows.\n",
        "\n",
        "VI can be used to estimate Bayesian [credible intervals](https://en.wikipedia.org/wiki/Credible_interval) for parameters of a regression model to estimate the effects of various treatments or observed features on an outcome of interest. Credible intervals bound the values of an unobserved parameter with a certain probability, according to the posterior distribution of the parameter conditioned on observed data and given an assumption on the parameter's prior distribution.\n",
        "\n",
        "In this Colab, we demonstrate how to use VI to obtain credible intervals for parameters of a Bayesian linear regression model for radon levels measured in homes (using [Gelman et al.'s (2007) Radon dataset](http://www.stat.columbia.edu/~gelman/arm/); see [similar examples](https://mc-stan.org/users/documentation/case-studies/radon.html#Correlations-among-levels) in Stan). We demonstrate how TFP `JointDistribution`s combine with `bijectors` to build and fit two types of expressive surrogate posteriors:\n",
        "\n",
        "- a standard Normal distribution transformed by a block matrix.  The matrix may reflect independence among some components of the posterior and dependence among others, relaxing the assumption of a mean-field or full-covariance posterior.\n",
        "- a more complex, higher-capacity [inverse autoregressive flow](https://arxiv.org/abs/1606.04934).\n",
        "\n",
        "The surrogate posteriors are trained and compared with results from a mean-field surrogate posterior baseline, as well as ground-truth samples from Hamiltonian Monte Carlo."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pt5Lzw4hjd6A"
      },
      "source": [
        "## Overview of Bayesian Variational Inference\n",
        "\n",
        "Suppose we have the following generative process, where $\\theta$ represents random parameters, $\\omega$ represents deterministic parameters, and the $x_i$ are features and the $y_i$ are target values for $i=1,\\ldots,n$ observed data points:\n",
        "\\begin{align*}\n",
        "&\\theta \\sim r(\\Theta) && \\text{(Prior)}\\\\\n",
        "&\\text{for } i = 1 \\ldots n: \\nonumber \\\\\n",
        "&\\quad y_i \\sim p(Y_i|x_i, \\theta, \\omega) && \\text{(Likelihood)}\n",
        "\\end{align*}\n",
        "\n",
        "VI is then characterized by:\n",
        "$\\newcommand{\\E}{\\operatorname{\\mathbb{E}}}\n",
        "\\newcommand{\\K}{\\operatorname{\\mathbb{K}}}\n",
        "\\newcommand{\\defeq}{\\overset{\\tiny\\text{def}}{=}}\n",
        "\\DeclareMathOperator*{\\argmin}{arg\\,min}$\n",
        "\n",
        "\\begin{align*}\n",
        "-\\log p(\\{y_i\\}_i^n|\\{x_i\\}_i^n, \\omega)\n",
        "&\\defeq -\\log \\int \\textrm{d}\\theta\\, r(\\theta) \\prod_i^n p(y_i|x_i,\\theta, \\omega) && \\text{(Really hard integral)} \\\\\n",
        "&= -\\log \\int \\textrm{d}\\theta\\, q(\\theta) \\frac{1}{q(\\theta)} r(\\theta) \\prod_i^n p(y_i|x_i,\\theta, \\omega) && \\text{(Multiply by 1)}\\\\\n",
        "&\\le - \\int \\textrm{d}\\theta\\, q(\\theta) \\log \\frac{r(\\theta) \\prod_i^n p(y_i|x_i,\\theta, \\omega)}{q(\\theta)}  && \\text{(Jensen's inequality)}\\\\\n",
        "&\\defeq \\E_{q(\\Theta)}[ -\\log p(y_i|x_i,\\Theta, \\omega) ] + \\K[q(\\Theta), r(\\Theta)]\\\\\n",
        "&\\defeq ``\\text{expected negative log likelihood\"} + ``\\text{kl regularizer\"}\n",
        "\\end{align*}\n",
        "\n",
        "(Technically we're assuming $q$ is [absolutely continuous](https://en.wikipedia.org/wiki/Absolute_continuity#Absolute_continuity_of_measures) with respect to $r$. See also, [Jensen's inequality](https://en.wikipedia.org/wiki/Jensen%27s_inequality).)\n",
        "\n",
        "Since the bound holds for all q, it is obviously tightest for:\n",
        "\n",
        "$$q^*,w^* = \\argmin_{q \\in \\mathcal{Q},\\omega\\in\\mathbb{R}^d} \\left\\{ \\sum_i^n\\E_{q(\\Theta)}\\left[ -\\log p(y_i|x_i,\\Theta, \\omega) \\right] + \\K[q(\\Theta), r(\\Theta)] \\right\\}$$\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "Regarding terminology, we call\n",
        "\n",
        "- $q^*$ the \"surrogate posterior,\" and,\n",
        "- $\\mathcal{Q}$ the \"surrogate family.\"\n",
        "\n",
        "$\\omega^*$ represents the maximum-likelihood values of the deterministic parameters on the VI loss. See [this survey](https://arxiv.org/abs/1601.00670) for more information on variational inference."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pt532xMzBJiR"
      },
      "source": [
        "## Example: Bayesian hierarchical linear regression on Radon measurements\n",
        "\n",
        "Radon is a radioactive gas that enters homes through contact points with the\n",
        "ground. It is a carcinogen that is the primary cause of lung cancer in\n",
        "non-smokers. Radon levels vary greatly from household to household.\n",
        "\n",
        "The EPA did a study of radon levels in 80,000 houses. Two important predictors\n",
        "are:\n",
        "- Floor on which the measurement was taken (radon higher in basements)\n",
        "- County uranium level (positive correlation with radon levels)\n",
        "\n",
        "Predicting radon levels in houses grouped by county is a classic problem in Bayesian hierarchical modeling, introduced by [Gelman and Hill (2006)](http://www.stat.columbia.edu/~gelman/arm/). We will build a hierarchical linear model to predict radon measurements in houses, in which the hierarchy is the grouping of houses by county. We are interested in credible intervals for the effect of location (county) on the radon level of houses in Minnesota. In order to isolate this effect, the effects of floor and uranium level are also included in the model. Additionaly, we will incorporate a contextual effect corresponding to the mean floor on which the measurement was taken, by county, so that if there is variation among counties of the floor on which the measurements were taken, this is not attributed to the county effect."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "i00BTGk5tiwe"
      },
      "outputs": [],
      "source": [
        "!pip3 install -q tf-nightly tfp-nightly"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "H9omoz32_Y9F"
      },
      "outputs": [],
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import seaborn as sns\n",
        "import tensorflow as tf\n",
        "import tensorflow_datasets as tfds\n",
        "import tensorflow_probability as tfp\n",
        "import warnings\n",
        "\n",
        "tfd = tfp.distributions\n",
        "tfb = tfp.bijectors\n",
        "\n",
        "plt.rcParams['figure.facecolor'] = '1.'"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "BFKYEEfY1FhB"
      },
      "outputs": [],
      "source": [
        "# Load the Radon dataset from `tensorflow_datasets` and filter to data from\n",
        "# Minnesota.\n",
        "dataset = tfds.as_numpy(\n",
        "    tfds.load('radon', split='train').filter(\n",
        "        lambda x: x['features']['state'] == 'MN').batch(10**9))\n",
        "\n",
        "# Dependent variable: Radon measurements by house.\n",
        "dataset = next(iter(dataset))\n",
        "radon_measurement = dataset['activity'].astype(np.float32)\n",
        "radon_measurement[radon_measurement <= 0.] = 0.1\n",
        "log_radon = np.log(radon_measurement)\n",
        "\n",
        "# Measured uranium concentrations in surrounding soil.\n",
        "uranium_measurement = dataset['features']['Uppm'].astype(np.float32)\n",
        "log_uranium = np.log(uranium_measurement)\n",
        "\n",
        "# County indicator.\n",
        "county_strings = dataset['features']['county'].astype('U13')\n",
        "unique_counties, county = np.unique(county_strings, return_inverse=True)\n",
        "county = county.astype(np.int32)\n",
        "num_counties = unique_counties.size\n",
        "\n",
        "# Floor on which the measurement was taken.\n",
        "floor_of_house = dataset['features']['floor'].astype(np.int32)\n",
        "\n",
        "# Average floor by county (contextual effect).\n",
        "county_mean_floor = []\n",
        "for i in range(num_counties):\n",
        "  county_mean_floor.append(floor_of_house[county == i].mean())\n",
        "county_mean_floor = np.array(county_mean_floor, dtype=log_radon.dtype)\n",
        "floor_by_county = county_mean_floor[county]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EU9ieWyOjddQ"
      },
      "source": [
        "The regression model is specified as follows:\n",
        "\n",
        "$\\newcommand{\\Normal}{\\operatorname{\\sf Normal}}$\n",
        "\\begin{align*}\n",
        "&\\text{uranium_weight}  \\sim \\Normal(0, 1) \\\\\n",
        "&\\text{county_floor_weight}  \\sim \\Normal(0, 1) \\\\\n",
        "&\\text{for } j = 1\\ldots \\text{num_counties}:\\\\\n",
        "&\\quad \\text{county_effect}_j  \\sim \\Normal (0, \\sigma_c)\\\\\n",
        "&\\text{for } i = 1\\ldots n:\\\\\n",
        "&\\quad \\mu_i  = ( \\\\\n",
        "&\\quad\\quad \\text{bias} \\\\\n",
        "&\\quad\\quad + \\text{county_effect}_{\\text{county}_i}  \\\\\n",
        "&\\quad\\quad +\\text{log_uranium}_i \\times  \\text{uranium_weight} \\\\\n",
        "&\\quad\\quad +\\text{floor_of_house}_i \\times \\text{floor_weight} \\\\ \n",
        "&\\quad\\quad +\\text{floor_by_county}_{\\text{county}_i} \\times \\text{county_floor_weight} ) \\\\\n",
        "&\\quad \\text{log_radon}_i  \\sim \\Normal(\\mu_i, \\sigma_y)\n",
        "\\end{align*}\n",
        "in which $i$ indexes the observations and $\\text{county}_i$ is the county in which the $i$th observation was taken.\n",
        "\n",
        "We use a county-level random effect to capture geographical variation. The parameters `uranium_weight` and `county_floor_weight` are modeled probabilistically, and `floor_weight` and the constant `bias` are deterministic.  These modeling choices are largely arbitrary, and are made for the purpose of demonstrating VI on a probabilistic model of reasonable complexity. For a more thorough discussion of multilevel modeling with fixed and random effects in TFP, using the radon dataset, see [Multilevel Modeling Primer](https://github.com/tensorflow/probability/blob/main/tensorflow_probability/examples/jupyter_notebooks/Multilevel_Modeling_Primer.ipynb) and [Fitting Generalized Linear Mixed-effects Models Using Variational Inference](https://github.com/tensorflow/probability/blob/main/tensorflow_probability/examples/jupyter_notebooks/Linear_Mixed_Effects_Model_Variational_Inference.ipynb)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "awL6fCUh6OCF"
      },
      "outputs": [],
      "source": [
        "# Create variables for fixed effects.\n",
        "floor_weight = tf.Variable(0.)\n",
        "bias = tf.Variable(0.)\n",
        "\n",
        "# Variables for scale parameters.\n",
        "log_radon_scale = tfp.util.TransformedVariable(1., tfb.Exp())\n",
        "county_effect_scale = tfp.util.TransformedVariable(1., tfb.Exp())\n",
        "\n",
        "# Define the probabilistic graphical model as a JointDistribution.\n",
        "@tfd.JointDistributionCoroutineAutoBatched\n",
        "def model():\n",
        "  uranium_weight = yield tfd.Normal(0., scale=1., name='uranium_weight')\n",
        "  county_floor_weight = yield tfd.Normal(\n",
        "      0., scale=1., name='county_floor_weight')\n",
        "  county_effect = yield tfd.Sample(\n",
        "      tfd.Normal(0., scale=county_effect_scale),\n",
        "      sample_shape=[num_counties], name='county_effect')\n",
        "  yield tfd.Normal(\n",
        "      loc=(log_uranium * uranium_weight + floor_of_house* floor_weight\n",
        "           + floor_by_county * county_floor_weight\n",
        "           + tf.gather(county_effect, county, axis=-1)\n",
        "           + bias),\n",
        "      scale=log_radon_scale[..., tf.newaxis],\n",
        "      name='log_radon') \n",
        "\n",
        "# Pin the observed `log_radon` values to model the un-normalized posterior.\n",
        "target_model = model.experimental_pin(log_radon=log_radon)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UlkQTJSlkjJ1"
      },
      "source": [
        "## Expressive surrogate posteriors\n",
        "\n",
        "Next we estimate the posterior distributions of the random effects using VI with two different types of surrogate posteriors:\n",
        "- A constrained multivariate Normal distribution, with covariance structure induced by a blockwise matrix transformation.\n",
        "- A multivariate Standard Normal distribution transformed by an [Inverse Autoregressive Flow](https://arxiv.org/abs/1606.04934), which is then split and restructured to match the support of the posterior."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3QG0scmDcdTw"
      },
      "source": [
        "### Multivariate Normal surrogate posterior"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "K8soBr2oBHSV"
      },
      "source": [
        "To build this surrogate posterior, a trainable linear operator is used to induce correlation among the components of the posterior."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "sJuvC5ykBAiK"
      },
      "outputs": [],
      "source": [
        "# Determine the `event_shape` of the posterior, and calculate the size of each\n",
        "# `event_shape` component. These determine the sizes of the components of the\n",
        "# underlying standard Normal distribution, and the dimensions of the blocks in\n",
        "# the blockwise matrix transformation.\n",
        "event_shape = target_model.event_shape_tensor()\n",
        "flat_event_shape = tf.nest.flatten(event_shape)\n",
        "flat_event_size = tf.nest.map_structure(tf.reduce_prod, flat_event_shape)\n",
        "\n",
        "# The `event_space_bijector` maps unconstrained values (in R^n) to the support\n",
        "# of the prior -- we'll need this at the end to constrain Multivariate Normal\n",
        "# samples to the prior's support.\n",
        "event_space_bijector = target_model.experimental_default_event_space_bijector()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LxLqBKBgsQPg"
      },
      "source": [
        "Construct a `JointDistribution` with vector-valued standard Normal components, with sizes determined by the corresponding prior components. The components should be vector-valued so they can be transformed by the linear operator."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "0ceaCfU8sPjg"
      },
      "outputs": [],
      "source": [
        "base_standard_dist = tfd.JointDistributionSequential(\n",
        "      [tfd.Sample(tfd.Normal(0., 1.), s) for s in flat_event_size])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uu0d8uWS4luv"
      },
      "source": [
        "Build a trainable blockwise lower-triangular linear operator. We'll apply it to the standard Normal distribution to implement a (trainable) blockwise matrix transformation and induce the correlation structure of the posterior.\n",
        "\n",
        "Within the blockwise linear operator, a trainable full-matrix block represents full covariance between two components of the posterior, while a block of zeros (or `None`) expresses independence. Blocks on the diagonal are either lower-triangular or diagonal matrices, so that the entire block structure represents a lower-triangular matrix.\n",
        "\n",
        "Applying this bijector to the base distribution results in a multivariate Normal distribution with mean 0 and (Cholesky-factored) covariance equal to the lower-triangular block matrix."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "dUCks9qg6nU2"
      },
      "outputs": [],
      "source": [
        "operators = (\n",
        "    (tf.linalg.LinearOperatorDiag,),  # Variance of uranium weight (scalar).\n",
        "    (tf.linalg.LinearOperatorFullMatrix,  # Covariance between uranium and floor-by-county weights.\n",
        "     tf.linalg.LinearOperatorDiag),  # Variance of floor-by-county weight (scalar).\n",
        "    (None,  # Independence between uranium weight and county effects.\n",
        "     None,  #  Independence between floor-by-county and county effects.\n",
        "     tf.linalg.LinearOperatorDiag)  # Independence among the 85 county effects.\n",
        "    )\n",
        "\n",
        "block_tril_linop = (\n",
        "    tfp.experimental.vi.util.build_trainable_linear_operator_block(\n",
        "        operators, flat_event_size))\n",
        "scale_bijector = tfb.ScaleMatvecLinearOperatorBlock(block_tril_linop)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dHI0bziq44od"
      },
      "source": [
        "After applying the linear operator to the standard Normal distribution, apply a multipart `Shift` bijector to allow the mean to take nonzero values."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ceS386lN448r"
      },
      "outputs": [],
      "source": [
        "loc_bijector = tfb.JointMap(\n",
        "    tf.nest.map_structure(\n",
        "        lambda s: tfb.Shift(\n",
        "            tf.Variable(tf.random.uniform(\n",
        "                (s,), minval=-2., maxval=2., dtype=tf.float32))),\n",
        "        flat_event_size))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gLO_8C0_Hd7f"
      },
      "source": [
        "The resulting multivariate Normal distribution, obtained by transforming the standard Normal distribution with the scale and location bijectors, must be reshaped and restructured to match the prior, and finally constrained to the support of the prior."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "PnnU3lJ7H-pj"
      },
      "outputs": [],
      "source": [
        "# Reshape each component to match the prior, using a nested structure of\n",
        "# `Reshape` bijectors wrapped in `JointMap` to form a multipart bijector.\n",
        "reshape_bijector = tfb.JointMap(\n",
        "    tf.nest.map_structure(tfb.Reshape, flat_event_shape))\n",
        "\n",
        "# Restructure the flat list of components to match the prior's structure\n",
        "unflatten_bijector = tfb.Restructure(\n",
        "        tf.nest.pack_sequence_as(\n",
        "            event_shape, range(len(flat_event_shape))))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HK3n0iqc5Ei3"
      },
      "source": [
        "Now, put it all together -- chain the trainable bijectors together and apply them to the base standard Normal distribution to construct the surrogate posterior."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "xlrIbELO5EWR"
      },
      "outputs": [],
      "source": [
        "surrogate_posterior = tfd.TransformedDistribution(\n",
        "    base_standard_dist,\n",
        "    bijector = tfb.Chain(  # Note that the chained bijectors are applied in reverse order\n",
        "        [\n",
        "         event_space_bijector,  # constrain the surrogate to the support of the prior\n",
        "         unflatten_bijector,  # pack the reshaped components into the `event_shape` structure of the posterior\n",
        "         reshape_bijector,  # reshape the vector-valued components to match the shapes of the posterior components\n",
        "         loc_bijector,  # allow for nonzero mean\n",
        "         scale_bijector  # apply the block matrix transformation to the standard Normal distribution\n",
        "         ]))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bVmf3qld5oPP"
      },
      "source": [
        "Train the multivariate Normal surrogate posterior."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "J5c5mhh-F9l-"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Multivariate Normal surrogate posterior ELBO: -1065.705322265625\n"
          ]
        },
        {
          "data": {
            "image/png": 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GDFy9ehWPPPKI4ob1er33oVE6nQ6xsbGw2+3Yt28fjh49CgB46qmn8POf/xxvvPEG9u3b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\neBARUY/9f4IYoj+gmvdcAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 600x400 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "optimizer = tf.optimizers.Adam(learning_rate=1e-2)\n",
        "@tf.function(jit_compile=True)\n",
        "def fit_vi():\n",
        "  return tfp.vi.fit_surrogate_posterior(\n",
        "      target_model.unnormalized_log_prob,\n",
        "      surrogate_posterior,\n",
        "      optimizer=optimizer,\n",
        "      num_steps=10**4,\n",
        "      sample_size=16,\n",
        "      )\n",
        "mvn_loss = fit_vi()\n",
        "\n",
        "mvn_samples = surrogate_posterior.sample(1000)\n",
        "mvn_final_elbo = tf.reduce_mean(\n",
        "    target_model.unnormalized_log_prob(*mvn_samples)\n",
        "    - surrogate_posterior.log_prob(mvn_samples))\n",
        "\n",
        "print('Multivariate Normal surrogate posterior ELBO: {}'.format(mvn_final_elbo))\n",
        "\n",
        "plt.plot(mvn_loss)\n",
        "plt.xlabel('Training step')\n",
        "_ = plt.ylabel('Loss value')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_Wh2eps0fQCZ"
      },
      "source": [
        "Since the trained surrogate posterior is a TFP distribution, we can take samples from it and process them to produce posterior credible intervals for the parameters.\n",
        "\n",
        "The box-and-whiskers plots below show 50% and 95% [credible intervals](https://en.wikipedia.org/wiki/Credible_interval) for the county effect of the two largest counties and the regression weights on soil uranium measurements and mean floor by county. The posterior credible intervals for county effects indicate that location in St. Louis county is associated with lower radon levels, after accounting for other variables, and that the effect of location in Hennepin county is near neutral.\n",
        "\n",
        "Posterior credible intervals on the regression weights show that higher levels of soil uranium are associated with higher radon levels, and counties where measurements were taken on higher floors (likely because the house didn't have a basement) tend to have higher levels of radon, which could relate to soil properties and their effect on the type of structures built.\n",
        "\n",
        "The (deterministic) coefficient of floor is negative, indicating that lower floors have higher radon levels, as expected."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "600DiJ8xfQf-"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Bias is: 1.40\n",
            "Floor fixed effect is: -0.72\n"
          ]
        },
        {
          "data": {
            "image/png": 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ffmiGKMkYISEhOuXQ0FAzRUKGapdte+jWoe9+TLJ8rW2t1a9fPxQXFzdp17t3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\nsIZe+cFuNQAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 1600x400 with 4 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "st_louis_co = 69  # Index of St. Louis, the county with the most observations.\n",
        "hennepin_co = 25  # Index of Hennepin, with the second-most observations.\n",
        "\n",
        "def pack_samples(samples):\n",
        "  return {'County effect (St. Louis)': samples.county_effect[..., st_louis_co],\n",
        "          'County effect (Hennepin)': samples.county_effect[..., hennepin_co],\n",
        "          'Uranium weight': samples.uranium_weight,\n",
        "          'Floor-by-county weight': samples.county_floor_weight}\n",
        "\n",
        "def plot_boxplot(posterior_samples):\n",
        "  fig, axes = plt.subplots(1, 4, figsize=(16, 4))\n",
        "\n",
        "  # Invert the results dict for easier plotting.\n",
        "  k = list(posterior_samples.values())[0].keys()\n",
        "  plot_results = {\n",
        "      v: {p: posterior_samples[p][v] for p in posterior_samples} for v in k}\n",
        "  for i, (var, var_results) in enumerate(plot_results.items()):\n",
        "    sns.boxplot(data=list(var_results.values()), ax=axes[i],\n",
        "                width=0.18*len(var_results), whis=(2.5, 97.5))\n",
        "    # axes[i].boxplot(list(var_results.values()), whis=(2.5, 97.5))\n",
        "    axes[i].title.set_text(var)\n",
        "    fs = 10 if len(var_results) < 4 else 8\n",
        "    axes[i].set_xticklabels(list(var_results.keys()), fontsize=fs)\n",
        "\n",
        "results = {'Multivariate Normal': pack_samples(mvn_samples)}\n",
        "\n",
        "print('Bias is: {:.2f}'.format(bias.numpy()))\n",
        "print('Floor fixed effect is: {:.2f}'.format(floor_weight.numpy()))\n",
        "plot_boxplot(results)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WnWb8WSDcjEK"
      },
      "source": [
        "### Inverse Autoregressive Flow surrogate posterior"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SUHcK4WzJ27o"
      },
      "source": [
        "Inverse Autoregressive Flows (IAFs) are normalizing flows that use neural networks to capture complex, nonlinear dependencies among components of the distribution. Next we build an IAF surrogate posterior to see whether this higher-capacity, more fiexible model outperforms the constrained multivariate Normal."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "R0FFLYnaGRrc"
      },
      "outputs": [],
      "source": [
        "# Build a standard Normal with a vector `event_shape`, with length equal to the\n",
        "# total number of degrees of freedom in the posterior.\n",
        "base_distribution = tfd.Sample(\n",
        "    tfd.Normal(0., 1.), sample_shape=[tf.reduce_sum(flat_event_size)])\n",
        "\n",
        "# Apply an IAF to the base distribution.\n",
        "num_iafs = 2\n",
        "iaf_bijectors = [\n",
        "    tfb.Invert(tfb.MaskedAutoregressiveFlow(\n",
        "        shift_and_log_scale_fn=tfb.AutoregressiveNetwork(\n",
        "            params=2, hidden_units=[256, 256], activation='relu')))\n",
        "    for _ in range(num_iafs)\n",
        "]\n",
        "\n",
        "# Split the base distribution's `event_shape` into components that are equal\n",
        "# in size to the prior's components.\n",
        "split = tfb.Split(flat_event_size)\n",
        "\n",
        "# Chain these bijectors and apply them to the standard Normal base distribution\n",
        "# to build the surrogate posterior. `event_space_bijector`,\n",
        "# `unflatten_bijector`, and `reshape_bijector` are the same as in the\n",
        "# multivariate Normal surrogate posterior.\n",
        "iaf_surrogate_posterior = tfd.TransformedDistribution(\n",
        "    base_distribution,\n",
        "    bijector=tfb.Chain([\n",
        "         event_space_bijector,  # constrain the surrogate to the support of the prior\n",
        "         unflatten_bijector,  # pack the reshaped components into the `event_shape` structure of the prior\n",
        "         reshape_bijector,  # reshape the vector-valued components to match the shapes of the prior components\n",
        "         split] +  # Split the samples into components of the same size as the prior components\n",
        "         iaf_bijectors  # Apply a flow model to the Tensor-valued standard Normal distribution\n",
        "         ))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "j4pzY9dPrBny"
      },
      "source": [
        "Train the IAF surrogate posterior."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "WyQayFhIz1Bq"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "IAF surrogate posterior ELBO: -1065.3663330078125\n"
          ]
        },
        {
          "data": {
            "image/png": 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urubw4cMsW7YMgGeffZaEhATuvvtuGhoaAHC73cydO9fbx26343a7cbvd2O32i9oDSVMe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\ngg==\n",
            "text/plain": [
              "<Figure size 600x400 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "optimizer=tf.optimizers.Adam(learning_rate=1e-2)\n",
        "@tf.function(jit_compile=True)\n",
        "def fit_vi():\n",
        "  return tfp.vi.fit_surrogate_posterior(\n",
        "    target_model.unnormalized_log_prob,\n",
        "    iaf_surrogate_posterior,\n",
        "    optimizer=optimizer,\n",
        "    num_steps=10**4,\n",
        "    sample_size=4\n",
        "    )\n",
        "iaf_loss = fit_vi()\n",
        "\n",
        "iaf_samples = iaf_surrogate_posterior.sample(1000)\n",
        "iaf_final_elbo = tf.reduce_mean(\n",
        "    target_model.unnormalized_log_prob(*iaf_samples)\n",
        "    - iaf_surrogate_posterior.log_prob(iaf_samples))\n",
        "print('IAF surrogate posterior ELBO: {}'.format(iaf_final_elbo))\n",
        "\n",
        "plt.plot(iaf_loss)\n",
        "plt.xlabel('Training step')\n",
        "_ = plt.ylabel('Loss value')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tzrbAezxPLeB"
      },
      "source": [
        "The credible intervals for the IAF surrogate posterior appear similar to those of the constrained multivariate Normal."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "QmKl4G1BGIIl"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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EdXU1W10lYIkTe7RmErQ9e/Zg48aNWLNmTau25eRp1F6io6NVT+vZFbTlbojX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\norHhSkRERERERIr2f9JDSr8a5p0QAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 1600x400 with 4 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "results['IAF'] = pack_samples(iaf_samples)\n",
        "plot_boxplot(results)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IWKqLYPOZOO_"
      },
      "source": [
        "### Baseline: Mean-field surrogate posterior\n",
        "\n",
        "VI surrogate posteriors are often assumed to be mean-field (independent) Normal distributions, with trainable means and variances, that are constrained to the support of the prior with a bijective transformation. We define a mean-field surrogate posterior in addition to the two more expressive surrogate posteriors, using the same general formula as the multivariate Normal surrogate posterior."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "GoPeLGAjZLbS"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Mean-field surrogate posterior ELBO: -1065.7652587890625\n"
          ]
        },
        {
          "data": {
            "image/png": 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4/s4dRuCDFPiiWFjBD+cX9V8xakh/Eh12fJ1fjK6dk4HgJ9zQ2eswhlavH4vO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\nAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 600x400 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# A block-diagonal linear operator, in which each block is a diagonal operator,\n",
        "# transforms the standard Normal base distribution to produce a mean-field\n",
        "# surrogate posterior.\n",
        "operators = (tf.linalg.LinearOperatorDiag,\n",
        "             tf.linalg.LinearOperatorDiag,\n",
        "             tf.linalg.LinearOperatorDiag)\n",
        "block_diag_linop = (\n",
        "    tfp.experimental.vi.util.build_trainable_linear_operator_block(\n",
        "        operators, flat_event_size))\n",
        "mean_field_scale = tfb.ScaleMatvecLinearOperatorBlock(block_diag_linop)\n",
        "\n",
        "mean_field_loc = tfb.JointMap(\n",
        "    tf.nest.map_structure(\n",
        "        lambda s: tfb.Shift(\n",
        "            tf.Variable(tf.random.uniform(\n",
        "                (s,), minval=-2., maxval=2., dtype=tf.float32))),\n",
        "        flat_event_size))\n",
        "\n",
        "mean_field_surrogate_posterior = tfd.TransformedDistribution(\n",
        "    base_standard_dist,\n",
        "    bijector = tfb.Chain(  # Note that the chained bijectors are applied in reverse order\n",
        "        [\n",
        "         event_space_bijector,  # constrain the surrogate to the support of the prior\n",
        "         unflatten_bijector,  # pack the reshaped components into the `event_shape` structure of the posterior\n",
        "         reshape_bijector, # reshape the vector-valued components to match the shapes of the posterior components\n",
        "         mean_field_loc,   # allow for nonzero mean\n",
        "         mean_field_scale  # apply the block matrix transformation to the standard Normal distribution\n",
        "         ]))\n",
        "\n",
        "optimizer=tf.optimizers.Adam(learning_rate=1e-2)\n",
        "@tf.function(jit_compile=True)\n",
        "def fit_vi():\n",
        "  return tfp.vi.fit_surrogate_posterior(\n",
        "    target_model.unnormalized_log_prob,\n",
        "    mean_field_surrogate_posterior,\n",
        "    optimizer=optimizer,\n",
        "    num_steps=10**4,\n",
        "    sample_size=16)\n",
        "mean_field_loss = fit_vi()\n",
        "\n",
        "mean_field_samples = mean_field_surrogate_posterior.sample(1000)\n",
        "mean_field_final_elbo = tf.reduce_mean(\n",
        "    target_model.unnormalized_log_prob(*mean_field_samples)\n",
        "    - mean_field_surrogate_posterior.log_prob(mean_field_samples))\n",
        "print('Mean-field surrogate posterior ELBO: {}'.format(mean_field_final_elbo))\n",
        "\n",
        "plt.plot(mean_field_loss)\n",
        "plt.xlabel('Training step')\n",
        "_ = plt.ylabel('Loss value')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qv3VzGvMX83Q"
      },
      "source": [
        "In this case, the mean field surrogate posterior gives similar results to the more expressive surrogate posteriors, indicating that this simpler model may be adequate for the inference task."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "3_P2nrNSGiG5"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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8bIuJiYnRzR2rrKxkT4YKBQcHw87ODgBgZ2dn1gvfNGWO+XfffYft27dj06ZN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\ncSUiIiIiIiJFY8WViIiIiIiIFO3/8QZRe5K3v60AAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 1600x400 with 4 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "results['Mean Field'] = pack_samples(mean_field_samples)\n",
        "plot_boxplot(results)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6FtKcJUyTToh"
      },
      "source": [
        "### Ground truth: Hamiltonian Monte Carlo (HMC)\n",
        "\n",
        "We use HMC to generate \"ground truth\" samples from the true posterior, for comparison with results of the surrogate posteriors."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "bwTmpfxuC_A4"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Acceptance rate is 0.9008625149726868\n"
          ]
        }
      ],
      "source": [
        "num_chains = 8\n",
        "num_leapfrog_steps = 3\n",
        "step_size = 0.4\n",
        "num_steps=20000\n",
        "\n",
        "flat_event_shape = tf.nest.flatten(target_model.event_shape)\n",
        "enum_components = list(range(len(flat_event_shape)))\n",
        "bijector = tfb.Restructure(\n",
        "    enum_components,\n",
        "    tf.nest.pack_sequence_as(target_model.event_shape, enum_components))(\n",
        "        target_model.experimental_default_event_space_bijector())\n",
        "\n",
        "current_state = bijector(\n",
        "    tf.nest.map_structure(\n",
        "        lambda e: tf.zeros([num_chains] + list(e), dtype=tf.float32),\n",
        "    target_model.event_shape))\n",
        "\n",
        "hmc = tfp.mcmc.HamiltonianMonteCarlo(\n",
        "    target_log_prob_fn=target_model.unnormalized_log_prob,\n",
        "    num_leapfrog_steps=num_leapfrog_steps,\n",
        "    step_size=[tf.fill(s.shape, step_size) for s in current_state])\n",
        "\n",
        "hmc = tfp.mcmc.TransformedTransitionKernel(\n",
        "    hmc, bijector)\n",
        "hmc = tfp.mcmc.DualAveragingStepSizeAdaptation(\n",
        "    hmc,\n",
        "    num_adaptation_steps=int(num_steps // 2 * 0.8),\n",
        "    target_accept_prob=0.9)\n",
        "\n",
        "chain, is_accepted = tf.function(\n",
        "    lambda current_state: tfp.mcmc.sample_chain(\n",
        "        current_state=current_state,\n",
        "        kernel=hmc,\n",
        "        num_results=num_steps // 2,\n",
        "        num_burnin_steps=num_steps // 2,\n",
        "        trace_fn=lambda _, pkr:\n",
        "        (pkr.inner_results.inner_results.is_accepted),\n",
        "        ),\n",
        "    autograph=False,\n",
        "    jit_compile=True)(current_state)\n",
        "\n",
        "accept_rate = tf.reduce_mean(tf.cast(is_accepted, tf.float32))\n",
        "ess = tf.nest.map_structure(\n",
        "    lambda c: tfp.mcmc.effective_sample_size(\n",
        "        c,\n",
        "        cross_chain_dims=1,\n",
        "        filter_beyond_positive_pairs=True),\n",
        "    chain)\n",
        "\n",
        "r_hat = tf.nest.map_structure(tfp.mcmc.potential_scale_reduction, chain)\n",
        "hmc_samples = pack_samples(\n",
        "    tf.nest.pack_sequence_as(target_model.event_shape, chain))\n",
        "print('Acceptance rate is {}'.format(accept_rate))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GSRQTbT-T07X"
      },
      "source": [
        "Plot sample traces to sanity-check HMC results."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "z34B7sa05KX1"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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eEEfjAata386OFXtQkwaumAxDoLWxmZx4hOZf/xZf3ucxSCDpMQLOvpOOjVWN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\nR+JaEAtwngAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 1400x150 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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laiax6G+Dw0Ej/l62f1BP67L1dP7fA4gIltVvKJiWULtrF8vnPjLAoIyFNaLB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ImL8e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\nK7RlUwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 1400x150 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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u4en3agd5DiMvPYm26E7WPvpDfB1ustqzaNi8gVBHGw1bNvY3pNmKuq4aqMn+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\nIYQQQvgsSXiEEEIIIYQQPuv/A6soukFsBBi+AAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 1400x150 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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6xKFS73H3eb8r1KnIb13n9XNrWDVrz/4HKuV+vUo92bqsgfa6MAAOI05JRxkf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\nKlweTG7HiRRZ3nQsCVJjtnMw2GINjr9RFRlZZH1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5pzL9v/8NT9/+BHvaprFN6yU52EXX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\n",
            "text/plain": [
              "<Figure size 1400x150 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "def plot_traces(var_name, samples):\n",
        "  fig, axes = plt.subplots(1, 2, figsize=(14, 1.5), sharex='col', sharey='col')\n",
        "  for chain in range(num_chains):\n",
        "    s = samples.numpy()[:, chain]\n",
        "    axes[0].plot(s, alpha=0.7)\n",
        "    sns.kdeplot(s, ax=axes[1], shade=False)\n",
        "    axes[0].title.set_text(\"'{}' trace\".format(var_name))\n",
        "    axes[1].title.set_text(\"'{}' distribution\".format(var_name))\n",
        "    axes[0].set_xlabel('Iteration')\n",
        "\n",
        "warnings.filterwarnings('ignore')\n",
        "for var, var_samples in hmc_samples.items():\n",
        "  plot_traces(var, var_samples)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ioys0R7QYzH1"
      },
      "source": [
        "All three surrogate posteriors produced credible intervals that are visually similar to the HMC samples, though sometimes under-dispersed due to the effect of the ELBO loss, as is common in VI."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "hZ1GUl1dJtpl"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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QyMwsWrRIUo6NjZUpEiLSZfTo0ZJyRESETJH8DxNXohbQ3iqGW8cQmZe9e/dK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\nBGanAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 1600x400 with 4 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "results['HMC'] = hmc_samples\n",
        "plot_boxplot(results)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "V8Y-O_CsT7vH"
      },
      "source": [
        "## Additional results\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "cellView": "form",
        "id": "OUnECXkG42uZ"
      },
      "outputs": [],
      "source": [
        "#@title Plotting functions\n",
        "\n",
        "plt.rcParams.update({'axes.titlesize': 'medium', 'xtick.labelsize': 'medium'})\n",
        "def plot_loss_and_elbo():\n",
        "  fig, axes = plt.subplots(1, 2, figsize=(12, 4))\n",
        "\n",
        "  axes[0].scatter([0, 1, 2],\n",
        "                  [mvn_final_elbo.numpy(),\n",
        "                  iaf_final_elbo.numpy(),\n",
        "                  mean_field_final_elbo.numpy()])\n",
        "  axes[0].set_xticks(ticks=[0, 1, 2])\n",
        "  axes[0].set_xticklabels(labels=[\n",
        "    'Multivariate Normal', 'IAF', 'Mean Field'])\n",
        "  axes[0].title.set_text('Evidence Lower Bound (ELBO)')\n",
        "\n",
        "  axes[1].plot(mvn_loss, label='Multivariate Normal')\n",
        "  axes[1].plot(iaf_loss, label='IAF')\n",
        "  axes[1].plot(mean_field_loss, label='Mean Field')\n",
        "  axes[1].set_ylim([1000, 4000])\n",
        "  axes[1].set_xlabel('Training step')\n",
        "  axes[1].set_ylabel('Loss (negative ELBO)')\n",
        "  axes[1].title.set_text('Loss')\n",
        "  plt.legend()\n",
        "  plt.show()\n",
        "\n",
        "plt.rcParams.update({'axes.titlesize': 'medium', 'xtick.labelsize': 'small'})\n",
        "def plot_kdes(num_chains=8):\n",
        "  fig, axes = plt.subplots(2, 2, figsize=(12, 8))\n",
        "  k = list(results.values())[0].keys()\n",
        "  plot_results = {\n",
        "      v: {p: results[p][v] for p in results} for v in k}\n",
        "  for i, (var, var_results) in enumerate(plot_results.items()):\n",
        "    ax = axes[i % 2, i // 2]\n",
        "    for posterior, posterior_results in var_results.items():\n",
        "      if posterior == 'HMC':\n",
        "        label = posterior\n",
        "        for chain in range(num_chains):\n",
        "          sns.kdeplot(\n",
        "              posterior_results[:, chain],\n",
        "              ax=ax, shade=False, color='k', linestyle=':', label=label)\n",
        "          label=None\n",
        "      else:\n",
        "        sns.kdeplot(\n",
        "            posterior_results, ax=ax, shade=False, label=posterior)\n",
        "        ax.title.set_text('{}'.format(var))\n",
        "    ax.legend()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WXzsxJcG1kPH"
      },
      "source": [
        "### Evidence Lower Bound (ELBO)\n",
        "\n",
        "IAF, by far the largest and most flexible surrogate posterior, converges to the highest Evidence Lower Bound (ELBO)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "cKf_nCvpxohJ"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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27NlDdnY2FouFhx9+GKDKumXDMKptr0pqaipRUVFERUVRWFh4yfFqxllEXIkS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\n",
            "text/plain": [
              "<Figure size 1200x400 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plot_loss_and_elbo()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5ag72K8X3tpJ"
      },
      "source": [
        "### Posterior samples\n",
        "\n",
        "Samples from each surrogate posterior, compared with HMC ground truth samples (a different visualization of the samples shown in the box plots)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "_yjwsHIoftLX"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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ntWeVZf6MScbbyQJbc6P7bqdbk26UaIvQM4vj8AXJxyweXxKzxcMQnxmPnlKP\npg2aPnBdCoWCIKcgjiQeoai0qAZ6J0TVajVLxvLlyxk7dize3t5ERkYya9as2myu1q1bt46QkJBy\n74WEhLBu3bo66pGoSnRaNFq0eFpVPmBOv1nEyb8y6VbNdHL/5Gvni7mBOQ2t42Tjn3jsScwWtS0+\nIx5XC1f0lfo1Ul+QYxD5JfmEJ4XXSH1CVKXWlmQAqNVqwsMf/x/i3NxcAC5dulTh2scff6z7d3Bw\n8MPqkriLqNQogCpnmPfHpaDVUu10cv+kr9Sni1MXdl3ax7HzqZSUatBTyXlA4vEkMVvUtviM+Dtm\nLqouf3t/9JX6hF0Po5NDpxqrV4h/kt/sol6KSo3C0cyxygNL/oxJxtrMAK8aWHMc3CSYIm0uBaqL\nnLmWdfcbhBDiCaTRakjKS6qR9cu3mOib4GPrw+Hrh2usTiEqIwNmUS+dTTuLh5VHpddKSjXsi0uh\naytblMrKNwRWR2eHzugp9NAzjybsoizLEEKIypRoSgBqJEPG7QIcAojLiCM1X/aRiNojA2ZR72QW\nZHIt9xoe1pUPmCOuZJKVX0wPtwdbjnGLmYEZHRp3wLhhjGz8E0KIKtwaMDezqNmc9QEOAQCEXX88\nj3IXjwcZMIt6Jz6zLG1RG8s2lV7fcy4JfZWCoJb3fyzrP3Vr0o1SVQonrsVSVKKpsXqFEKK+KNGW\noKfQw8HMoUbrdWvkRkPDhhxJPFKj9QpxOxkwi3onLiMOqDrP556YZDo0s8LcSJ/8/HwSExN117Ta\nvw8fKS0tvec2uzbpWnaPcRSnr2beT7eFEKJeK9GU4GTuhJ6yZvMNKBVKOjbuSNj1sHIxXIiaJANm\nUe/EZ8RjaWiJtXHFGeTLaTc5n5xL9za23Lx5E29vbz799FMAtm7dSpMmTUhLK1uHvGTJEoKCgsjK\nuvtGPntTe1pbuqFnFs0RWccshBAVlGpKcW7gXCt1d3LoREp+Cuczz9dK/ULIgPkeKBQKnnnmGd3r\nkpISbGxsGDhwYK22O3HiRJo1a4ZarUatVvPJJ58A0L9/fzIz7zyL6eLiQmpqxfW08+fPZ/HixbXS\n30dFXEYcLS1bVnrC355zZaf79XCzxdTUlEmTJtGvXz8A9u7dy7Vr1zhypOxrvaZNm9KsWTMaNGhw\nT+32dO6Oyvgv9l+8WENPIoS4HxKzHz1arZYSTUmtDZhvrWOWbBmittRqHub6wtTUlKioKPLz8zE2\nNmbXrl04Ojo+lLY//PBDhg8fXu69bdu2PZS2H0carYbzmecZ1nJYpdf3xCThZJiPXkEmYMrMmTPZ\nu3cvGo2Gp556CkdHRwYMGADSfpQnAAAgAElEQVTAyJEjGTlyJAD5+fnk5eVhZWVVZdvdmnTjs8jP\nOJMeRmFJTwz1VDX+fEKIu5OY/egp1hSjRVtrA2Z7U3uaWTQj7HoYEzwm1Eob4skmM8z3qF+/fmzd\nuhUoO251zJgxums3b95k0qRJ+Pv74+Pjw2+//QZAQkICQUFB+Pr64uvry+HDZX/5hoaGEhwczPDh\nw2nTpg1jx46t1rqr22cifvzxR9q3b49areall16qdN3te++9R+vWrenZs6fu2Nv66mrOVfJL8itd\nv5xTUMzRi+mk/7GCgIAACgsL2bBhAz169GDTpk307duXa9euAZCdna37f1JaWkpgYCDPPvvsHdtu\nZdmKhgY2aI1jiLwi65iFqEsSsx8tt46urq0BM0BA4wBOJJ2gsLSw1toQT67Haob5g2MfEJMeU6N1\ntmnUhrfav3XXcqNHj+bdd99l4MCBnD59mkmTJnHgwAGgLLh1796db7/9lszMTNq3b0/Pnj2xtbVl\n165dGBkZER8fz5gxY3SnaJ08eZKzZ8/i4OBAYGAghw4donPnzhXanTFjBgsWLABg9erVeHl56a6d\nO3eO9evXc+jQIfT19XnllVf43//+x/jx43VlTpw4wbp16zh58iQlJSX4+vrSrl3NnbL0qInPKMuQ\n0cqyVYVrB+JTKdFo+eD9RejnXMfQ0BBHR0cCAwOZPXs2u3bt4u2338bNzY3ExERefvllZs+ejbm5\nOVOnTr3rDJVCoaCrUxc25W/h4IUbdHCtejZaiCeBxGyJ2bdUGDDfiIL4nWBmBx5DwcD0gdvo5NCJ\nNTFrOJl8ko6NOz5wfULc7rEaMNclb29vEhISWLt2Lf379y93befOnWzevFm3zqygoIArV67g4ODA\nlClTiIyMRKVSERcXp7unffv2ODk5AWXH0SYkJFQafCv7eu+WPXv2cOLECfz9/YGyZQO2tuVzCx84\ncICQkBBMTEwAGDx48H1+Ao+HuIw4FCho3rB5hWu7zt7AwlifwUE+lJZ4kpKSQq9evdBoNIwePRof\nHx9GjhzJW2+9RXFxMd988w2bN29m0qRJTJ8+/Z7a7+kSzG8Xf2H3xSP8i8rzQAshap/E7EdLoaYQ\nhUKBrYktHPkcdsz8++KfC2DkD9DE/451nLicwZZT17mSnodDQyNG+zfF87bTWv3s/dBT6BF2PUwG\nzKLGPVYD5nuZVahNgwcPZvr06YSGhuoyKUDZZoZffvmF1q1blys/f/587OzsOHXqFBqNBiMjI901\nQ0ND3b9VKhUlJSXV7o9Wq2XChAm8//77dyxX2ea3+io+M56mDZpirGdc7v3CklJWL/0PDUvTcVv9\nCnp6emRnZzN48GA6duzIjBkz6Nu3Ly+//DJNmzYFoHXr1vz3v//F3d0dAI1Gw8cff0zDhg15/vnn\nK22/vX17lOhzKS+crLzxWJjo1+4DC/EIk5hd3pMcs4tKi9BT6KE8v6dssOw2CAYuhZRY+O1V+H4Q\nTNgMTdpXuDc5u4BZG6PYfS4JY30VzlYmHL2Yxo9HrvBmr1a81r0FCoUCU31T2tq2Jex6GNPaTauD\npxT1maxhroZJkyYxb968cl+xAfTp04fly5fr1rSdPHkSgKysLBo3boxSqWT16tXVyut7L3r06MHP\nP/9McnJZ5of09HQuX75crkyXLl3YuHEj+fn55OTksGXLlhrtw6MmLiOuwnIMrVbLv95ZSEFeDq6O\ndjRo0ID4+HiSk5NZsWIFnTt3xt/fnxYtWgBw9epVxo0bR1paGmlJ1zFOPQX7F3PjhxfZ9v0S9v/4\nIYR+AGc3Qn5GubZM9E1wt/RBaRrLwfNy6p8QdUli9qOjqLQIlVIFm6eCTRsY9g2YWoNLIDy3E8zt\nYe0YSL9U7r5zidkM+ewQB8+n8FbfNoTP6cmON7oQNqsHIT6OfLwrjq/2/52ZKKBxAOfSz5FekP6w\nH1HUczJgrgYnJydef/31Cu/PnTuX4uJivL298fT0ZO7cuQC88sorfP/993Ts2JG4uDhMTR98jdbt\n3N3dWbBgAb1798bb25tevXqVO4QDwNfXl1GjRqFWqxk2bBhBQUE12odHSV5xHleyr9CyYfkNf5mZ\nmXz76UcYGZuwZcMawsPDsbe3x97eHktLS44dO0ZMTEzZzLJWS7CbLS/2diP609H8tnUH3SfM4uvF\nc2n2/De85q/ih8EqCP0vbJgIi1uVzY5kXdO11695MCrDFLadO/OQPwEhxO0kZj8aNFpN2QyzVgM5\n16H/YtD7e8YeM1sYuwE0JbBmFBSU5b4/dD6V4Z8fRquFXyZ3YnJwc0wNy74Yb2Ckz8cj2zLAqzEf\n7IjhxOWyAXInh04AHLkup/6JmqXQPkLH4vj5+ek2WNxy7tw53Nzc6qhH4lH2z5+NqNQoxmwdw9Lg\npfRw7qF7/+uV3/DiC8/T99UFdHVSkZuby/Lly3n77beZObNsHV3G5WgsL2yEqJ/5YW8MT3sbo2rW\niW9jTInJ0GPOuwtZuHQFb7zxBnZ2dtzMTMUk+wKKMz/ByR9BqQeDloHXcK5kX2HAxgHoZ4Rw4vV/\n18uvV0VFlcWv+k5itrgXhSWFnM88T8HFG7Q7swgm7YDK4uKl/bA6BJr3ILLz5zz9zXGaNjJh1bPt\nsbcwqlgeyC0soffH+7AwMWDLlEAUCi1d1nehe9Pu/CfwP7X8ZOJxVt2YLTPMot7455HYUVFRLF26\nlC9XrUZhaEIbawNmz57Nt99+y/nz55kxYwZkXoFfXsDy+yDY/yEnMsyZsKmA72znoZj4O+tOpLNx\nz1FyihVoNBosLS3Zv38/9k2acfyGAgZ8BK8eBXsv+OU5OPwpTRs0pZGBI/n6ZzmXmFOXH4kQQtS5\nIk1Zhgw9TSl0nFz5YBmgWRfouxDi/yD8u39hbWbID89VPVgGMDPUY/YAd84lZvNLxFVUShUdGnfg\n8PXDcky2qFGP1aY/Ie4kPiMeYz1jnMzLdrKvW7eOFStWMHT+92S2uYh+fiKOjo6sXbsWm0aWcHgZ\n7FsECgX5bSexKKwYD7/O/PHHHLp27UrTpk15/vnnadOmDWq1mszMTDp27MiaNWsYOHDg3ycAWrrA\n+M3w6wuwczaYNCK4SRd+KdjAH9GXcXfwqrrTQghRz93Ki6yHAlr3u2PZ/LbPsmfXTp4v3siQoN7Y\nmFc9WL6lv5c9Xo4WrAi9wDBfJwIcAth1eReXsi7h2tC1Rp5BCJlhFvVGXEYcLRq2QKko+7Fu2rQp\n1tbWhF25SRdvV4YOGcy1a9c4eSwM1oyAPf8mr0lXePUYhoM+4Jdtf3LkyBF69+5Nfn4+Hh4ehIaG\n0qlTJ9zd3bGxscHJyYm9e/fy9NNP06ZNm78b1zOAYSvLZkh+n0afhs4olCX8Hn+wjj4NIYR4NBSV\nFqJCi9LApPza5Uos2HaON3PHkW3TDpvdb5Qt07gLhULBlO4tuJyWx7aoGwQ0lmOyRc2r1QGzi4sL\nXl5eqNVq/Pz8arMp8YTTarXlMmQUFRXx119/kZqeScKmj/lx+jCGDx/Oh+8vYIxiC1zaz9yrwbi+\ntQ9NA0eUSiXHjh3T5WVt2LAhc+bM4fTp0zg5OeHl5UVGRgYajYZVq1Zx7NgxLl26RHR09N+dUOnD\n8O/AyAKfg5+jRI+r+af5Kz2vLj4SIapNYraoDUXF+RhotaBvcsdyu6KT+N/RKzwb1IoGz/4MjVxh\nzWj469hd2+jlZoezlQmrwxJwMneiqXlTwhLDaugJhHgIM8x79+4lMjLyidsMIx6u1PxUMgszaWnZ\nkpiYGBo3boxGo0G/gTVFV6NxdnZhYP/+fPj+u2iun4Lh3xE08lWmTJlCQUEBQLmcqwCBgYFcunQJ\ntVrNpk2bcHBwIDExkc2bN7NlyxYCAgJ4++23y3fE1Br6f4jxjTO0NbBBZXqBP87eeFgfgxAPTGK2\nqGmFpUUYaBWgqnp2ObewhNkbz+DWuAFv9m4FJo1g/CYwt4Mfh8P1k3dsQ6lUMK6DM8cTMjiXmE2A\nQwDHbxynuLS4ph9HPKFkSYaoF25t+Gtl2Yq//voLV1dXnn/hJWzHfkjI/32EkZEhA1sq6NGklNyO\n/wL3wfTu3Zs5c+boTtSqjLm5Oebm5ixatIgrV67w9NNPExsby4ABA7h58ybvvfdexZvcBoNrNzqn\nJaAySuT3qPjaemwhhHikaTSllKDFUGVQ9WY/4LO950nOKeS9EE8M9VRlb5rbl+0PMbIoy55x486p\nOoe3c8JApeTnE1cJcAggvySfyJTImnwc8QSr1QGzQqGgd+/etGvXjq+++qo2m6pVZmZm5V6vWrWK\nKVOmAGUnQykUCs6fP6+7vmTJEhQKhW6GJjc3l5deeonmzZvj4eFBly5dOHr06MN7gCdAfEbZoLRl\nw5aEhYVx+vRpPvpqNWc/HMW+r/6NoVKLX+qv/DhrBM1C5lS7/sDAQHr27Mn06dO5cuUKFhYWzJo1\ni2XLlrF79+7yhRUK6DmfDjllh5qczYggKbvgQR9RiFonMVtidk0rKsoFwEC/6pzWydkFfHvwEiE+\njvg2tSx/sWGTshMA9U3ghyGQHFNlPZamBgS3tmHLqeu0s/VHpVARdl2WZYiaUasD5kOHDhEREcH2\n7dv57LPP2L+/4uL9r776Cj8/P/z8/EhJSanN7tQaLy8v1q1bp3v9888/645TBnj++edp1KgR8fHx\nnD17llWrVpGaKqfA1aS4jDhsjW1JvZpKUFAQRUVFfPb+HLRF+djbWHP8Xy1wsDKFAR/fcZajKi4u\nLuzYsYOMjAwuX77MmTNnePXVV9m7dy8ff/xxxRsc1Hg498BMo0XfJJbfTydWLCPEI0ZidhmJ2TWn\nsCgbAAND8yrLrAi9QIlGyxs9W1ZeoFEzmLClLN/9mpGQV/UpfkPUjiTnFBJ9tQh3K3dOJJ14oP4L\ncUutDpgdHBwAsLW1JSQkhGPHKi7cf/HFFwkPDyc8PBwbG5va7E6tGTp0KL/99hsAFy9exMLCQvcs\nFy5c4OjRoyxYsAClsuzjdnV1ZcCAAXXW3/ooPjOelpYtmTlzJqNHj2bpsuUYObTEf+gkIjcsQnFx\nL3SdWbYe7gFMmzYNV1dXfvzxR3bs2EHbtm05ePAgeXkVN/bpBb6OX34+lubn2HTyWiW1CfFokZgt\nMbumFRWXxcaqZpiz8opZf/wvQnwccba6w8mKVs1h9BrISYRNr0AVOZZ7uNliZqjHpshr+Nr6cib1\njC6tnRAPotYGzDdv3iQnJ0f37507d+Lp6fnA9QYHB7Nq1SoAiouLCQ4O5scffwQgLy+P4OBg1q9f\nD0BWVhbBwcH8+uuvAKSmphIcHMyWLVsAuHHj3jZj5efno1ardf/Nmzev3PUGDRrQpEkToqKiWLt2\nLaNGjdJdO3v2LGq1GpVK9UDPLapWrCnmQuYFLHPLDhUZPHgw896ZhwYVHk5WqPa9X5Yr2f/5B27L\nxcUFKysrFAoFO3bsYP/+/fTo0YOEhATdL2Cdph3pYGhNtl4eUUkJnE+WQ0zEo0tidhmJ2TVIq6Wo\ntBg9FKiUlX+eG078RX5xKc8Guty9Pic/6Dkf4rbDqbWVFjHSV9HHw57tUTfwtGpLsaaY6LToSssK\nUR21NmBOSkqic+fOtG3blvbt2zNgwAD69u1bW83VKmNjYyIjI3X/vfvuuxXKjB49mnXr1rFp0yZC\nQkLqoJdPrstZlynWFONo5IijoyNbtmwhOzOD0pw0VrzUBRIjIehfZbmSH5BSqeTIkSO8+eabrF27\nFnt7e9q2bcv06dOZOnUqRUVFfxdWKPBt/RQALUyPsunk9QduX4jaIjFb1LjifAoVWgxV+pVe1mi0\n/HjkMu2cLfFwsLi3OjtMhiYdYOdcyM+stMgQtQM5BSXkZpUdYhWRFHFf3RfidrV20p+rqyunTp2q\n8XpDQ0N1/9bX1y/32sTEpNxrCwuLcq+tra3Lvba3t6+xfg0aNIgZM2bg5+f39wlwgIeHB6dOnUKj\n0ei+3hM1KzYjFoCia0UUFRWRmpqKefN29B7/GsYnvgJzB/AeXWPtKRQKOnfuTEREBE2aNOGTTz6h\nefPm7N69GwOD8oPyVu1exDh+NS0bnmJT5DXe7NUKpbL6a6iFqG0Ss8tIzK5BRTkUKRQ00DOu9PL+\n+BQS0vKY1qvVvdepVEK/RfBVMBxaWjbj/A+dmlthZWrAgdgCXBq4cDL5zinphLgXEg1qiLGxMR98\n8AGzZ88u937z5s3x8/PjnXfe0Z1rHx8fX/Hre3Hf4jLiKLxcyKI5i7h58yYNLBpi1u15XunZCi7u\nBb9na2R2+XY9evTg6NGj7Nixg6lTpxIdHU1GRllWjOLiv/N+6hlb0la/Icl6KdzIyOHElYwa7YcQ\n4v5IzK59JYU5lKLAQK/y461/CLuMtZkh/TwbV69iBzV4DIVjKyG/YkzVUynp3saWvTHJqG18OJl8\nEo1Wcz+PIISODJhr0OjRo/H19a3w/sqVK7lx4wYtWrTAy8uLF154Qbe5Rjy42PRYbqy8gUql4vLl\ny5jYNsHUtgmds34HhQp8nqnxNs3NzZk1axatW7dm5cqVGBgYEB8fz5AhQ3jxxRfLlfWx9ydeX0WQ\n4Sk2yuY/IR4ZErNrkVb794Y/ZcUJi5ScQkJjkxnp54SB3n0MRYL+BUU5ZYPmSvR0tyO7oAQLRSuy\ni7K5lHWp+m0IcZtaW5JRn+Tm5pZ7PXHiRCZOnAiU5fSszO1fIzZo0ICvv/66lnon4jPj6TaxG9sX\nbkehUFBs7sjAFpYYnF4DbfpDg2rOXtyjGTNmsHTpUho3bsygQYMYN24c48ePx9vbu1w5n9ZD0Vzb\nTWebYyw71YF3Brn/nZhfCFHjJGY/AkoKKaJsht6wkhP+dkQlotHCYPV9/iFi7wUt+8CRFdBxMhiW\nz70d1NIaQz0l15NtATiTeobmDZvfX1tCIDPM4jGXWZBJcl4ykT9HUlxcTJ9BIRh3n8yzjU5Dfjr4\nPVdrbRsYGLBmzRpUKhWnT5/G0tKSbt26MW3atHLlvO39UAI3tbHkFxQQGvt45q4VQoh7VnyTov+f\n816/kk1/v59OpIWtGa3tqs7PXJXLly8TERGBNuhfZXE+ck2FMiYGenRuYc3ROCWm+qZEpUZV/xmE\nuI0MmMVj7dj5Y1xecZkr566gVqsJfnkBekoFvqmbwbIZNOtaq+0HBgYSGxuLoaEhOTk5bN++HY1G\nw+7duykoKDvdz1TflNamjpzSh34mMZKTWQhR/xXlUahQoq/SR6koP9RIyi7gWEI6A70bo7jHg6Q0\nmr/XIK9atYqOHTuSauwKjdVwYlWleZl7udtxLaMQF7NWnE09+0CPI4QMmMVjbeeBneQcK8sde+bM\nGXZEXKSPsxb9vw6D96iyHdW1yMTEhDlz5qBSqVAqlSQnJxMYGEivXr3YuHGjrpyPU2fOGBoy3jKS\nPeeSycovvkOtQgjxmCu+SZFSWelyjG1nEtFqYaD3vS3HSE9Pp1OnTmzduhWA8ePHs3379rLDZtpN\n5FLsGbgaXuG+7m62KBSgV+xMTEYMRaVFFcoIca8eiwGztooTfcST69bPhLGnMQrDshmKPv0HcSkH\nxpmdBLTg+dRD6cvAgQOJiIjgueeeo6CggOzsbFasWFEut6unTVvylQpMCo9RXFrC9jNyVLaovyRm\nP+E0GrTFBRTx94a/238mfj+dSBt7c1rYmlVRQXmfffYZV65cIT8/n5s3b+Ls7EyPHj0A2HTJiFaf\n5rLrm/9UuM/W3Ah1k4YkpthQoikhLiPuwZ9NPLEe+QGzkZERaWlpEoCFjlarJS0tDSMjI7at3Ya2\nSIufnx8DXi5LD+WTvQfsvMCm9UPpj7e3N0eOHOHs2bOcOHECW1tbJk+ejJHR36mUPK3LTkyLIZ++\nljckW4aotyRmC4rzKEGLBi0GKoNyMTs5p4ATlzMY4FX1Zuzi4mLef/99ioqK0Gg0GBoa4urqytix\nY1m4cCHPPPMML7zwAklJSfTqP5h5ozvQSXMUCrIq1NXTzY6LVxsByDpm8UAe+SwZTk5OXL16lZQU\n2Sgl/mZkZMQ3335DxJcRqFQqBg0axMlU8GuQjVFSRKXJ7GvT9evXCQsLw9ramv3795OQkMCmTZtw\ndnYmJCQE5wbOmOubEmWYywTTeEbHOXAtMx/HhpUn9BficSUxW1CYQ2FBJmkqFcXGxSSrkjEyMsLJ\nyYmNp8qON+/uZlvl7b///juzZs1i69atREVFERsby//93/8xZcoU9uzZQ8eOHcnOzsbZ2ZmtW7cy\nd9Fn8HV3SiN/Av9J5Y417+1ux4d/NMREZcGZ1DOMpuYOsRJPlkd+wKyvr0+zZs3quhviEZScnQz6\nUFpYir6hEYfOp7LE4STcADweznKMW7p27crAgQOJiYnB2dkZX19fVCoV3bt3JyQkBKVCibu1J1GF\nhbxVGA50ZXPkdSYHS5ojUb9IzBZseJafUo7zH1MFO4ftpLHZ37PJobHJ2DUwxL1xgypvDwkJYfPm\nzXzzzTdkZWWxc+dOQkJC+PXXXwHYu3cv6enpKJVKVCoVE2Z9wiK3FgwdO53RU/N4/fXXdXW1sDXD\n2cqUkpKmxKTH1N4zi3rvkV+SIURVNKYaKAQDQwPUPZ8ir6iUgIL94OgHls4PvT9PPfUUkydPpmXL\nlmRlZfHf//6XdevW6a57WnkSryyFpAg6O8D2KFnHLISoh66Fk9DADiOVEXamdrq3i0s1HIhLpVtr\n20qzY/z+++8sWLCAXr16MWTIEJo2bUpAQACZmZm4urrSrl07li9fjqGhIcbGxmzbto0FCxYQFhbG\nJ9FWtDDNw96k/Il+CoWCHm3sSM+w5kLmRdn4J+6bDJjFY+nzzz9n56adAHyy/BMik4pxUaXSIPMc\nuA+pkz6NGzeOjIwMfv75Z/T09PDy8ir3S8HT2pMStMQa6DPR7hKnr2ZxNSOvTvoqhBC1IjcFMq+Q\nYGiIcwPncinlwhMyyCksoVubissxSkpKmDJlCp9//jkHDhzA39+f1NRU7OzscHNz4+mnn+bEiRNc\nunSJlJQUXn75Za5du4aDgwOLFi3iv6t3McrLiFHO6RXq7uFmS3FeY0q1JVzIvFCrjy/qLxkwi8dO\nfn4+b7zxBlfjr6LQU9DUqSmHL6QxwSq6rECbAXXWt4CAALy8vCgqKmL8+PFMnjyZwYMHA39v/Dtj\nZklHTQQAO6Ju1FlfhRCixl0rS+92WVuIc4Py3/TtjU1GX6UgsIV1hdtSUlKYM2cOL730ElqtloiI\nCFatWsUnn3zCTz/9xKZNmxg/fjxt2rTB3d2dpk2bMmPGDL744guGDh3KnDlzWHbahE9XfMG6Nf8j\nNjZWV7e/SyOMtE0AZFmGuG8yYBaPHa1WS6tWrdBqtBgaG9LSzZuo61n0VBwHGzewqrt1we3atSM6\nOprBgwdjamrKF198QWFhIXl5ediZ2GFlZMXZRo6YXd1PGzszGTALIeqXq+EUK1RcK0jDxcKl3KU/\nY5Lp0MwKM8Py26d27dqFo6MjL7zwAu+//z7e3t6sWLGCRYsW4enpSa9evXjrrbdYuHAhPXr0oEuX\nLjz99NMsWrQIlUrF0aNH+fjjjzkYn8memAzGT5jAihUrdPUb6CkJcmkNGgMZMIv7JgNm8djJzs7G\ntrEtaCCgXwAXbqqw0ObglH2yTmeXARo1asS+ffvo378/N2/eZNiwYfzyyy+YmJigUCjwtPYkSqWF\nmymMc83jxJUMkrML6rTPQghRY66F85d9G0q1pbg0cPn77cx8zifnEtzapsIt77//PlqtlqCgIAYN\nGsTy5ct54YUXGDFiBHPmzGHQoEFMnjwZgISEBH799Vf++OMPAP71r38RFBSEg4MDWzb/Rl93SyyM\nVUybNq1cGz3cGlNaYE/Ejejae3ZRr8mAWTxWkpKSaN26NQl/JQAwddpUwi6k0dcgEoVWA24D67aD\ngK+vL19//TXx8fFcv34dpVJJXl7ZWmV3K3cSCtPJUyjobRKDVgt/nJVZZiFEPaDRwLUIEmzKsqTc\nPmAOu5AGUG45RlJSEhs3buTSpUs4OztjYGDA5s2bOX/+PACtW7dmxowZ5XLau7m5sX37dl0mDG9v\nb4YOHcq2bdvo2bsv+TZtcTYt5rMli9FoNLp84MGtbdAUOnAhK05yhIv7IgNm8VjZtGkT2dnZJMQn\ngBLat2jP4QupDDc9BQ0cobG6rrsIwKeffoqBgQFHjhwhICAAS0tLrly5gruVO1q0xFq7YJNyBFcb\nU3bIgFkIUR+kxUNhNgmmZQeFOFv8vYb58IVUGpka0NrOHChbWjdy5EhGjhzJ1atX8ff3JzExkWnT\npjFu3Lg7NtO3b1+MjIwoLCzkyy+/pFmzZrRs2ZKcnBymf7OXiBtaVnz5FdbW1gwbNgytVou1mSEO\nJs0p1uZxLVcOjhLVJwNm8Vhp3749AJpSDXb+dugbWnElKY22hRFlyzEqSVVUF9q3b8/o0aNZvnw5\np0+fxsLCAoVCgVsjNwCibV1RXD5Mfw9rjlxMJ/2mpDoSQjzmrv7/DX96KhoZNaKBQVmuZa1WS9iF\nNAJcrVAqFbr37O3tKSkpwdPTk+eee46TJ0/yzjvv3HNzSqWSXr16ERAQAMCff/5JaakGDwcTQt9o\nA8DmzZs5c+YMAIFOXgAcu3amZp5XPFFqfcBcWlqKj48PAwfW/Vfl4vGWlZVFVFQUnTp1AiB4TDDH\nLqUTpDyDvqagztcv306pVDJjxgzefvtt2rZty6lTp2jSpAm2JrZYGVkRbWwKhdkMsUmhVKNlX1xy\nXXdZCEBitngA18LB0IKEovRyyzES0vJIzCogoLkVAPPmzWPQoEGEhYUB8Morr9C9e3cMDAzKLb+4\nG319fRYuXMjQoUMBSEwsy23/5zf/xt/oMr06+wPQsGFDSktLObfmJ9L2ZrD7QmRNPK14wtT6gHnZ\nsmW4ubnVdjPiCTBz5oLoUvAAACAASURBVEzGjx9PcmoySmMlvbr14nhCOv30TqA1sgDnwLruYjlN\nmjShpKSEqKgo/h979x0ddZX+cfw9LZn03kglvZBCEnpPQhEBURABFVAssLrCsrq7oO6yi11RdIFd\nERQURFFX6QgCogRCSAKhJBDSGyG9ZzL198esKD9cRCSZlPs6h8Nx5jszHw85N8/c773P/dOf/kR2\ndjYNDQ2EOYWRrW0EIKA5HWdrMw5fEMcIC12DGLOFW1aaBp79KWwsoq/dj6c9HsurBmBogBNarZbt\n27eTk5NDSEgIa9eu5fnnn+fhhx/+zR8/ZswYVq9ejbL/vWTVSPli9wHkcjlnz55l6NChXMzMQFsp\n51y12Pgn/HodWjCXlpaye/duHnnkkY78GKGXuHLlCkqlktxLucicZPRz6cepwmqS5KeQBI0HmcLU\nEa9hZ2fH+++/j1Qq5auvviI8PJwNGzYQ7hROfmMRKrcIpIVHGBXsypGcKrQ6/S+/qSB0IDFmC7dM\n3QpXztPoEUWtqvaaHszH8mpwt1XS19kKmUyGUqmktraWsrIy3n77bT744AOWLFnymyOEhITwxBNP\nYOPmy/7GQHR6Ay7OTsyaNYuioiI8PDyIvX88tZpC2rW63/x5Qu/SoQXz4sWLee2115BK//fHrFu3\njvj4eOLj46mqErNswv8WHR2NSqVCKpHiOdsTH+sgrK6cxFbf2CW6Y/ycmTNnkpubi5eXFwqFAl9f\nX8Idw9EZdOR4RUPxCZKC7Gho03C6pN7UcYVeTozZwi27nAkGHUWOXsCPHTL0egMpeTUMDXDi5MmT\nzJs3DwcHB+rq6oiOjubdd9/ljjvuIDY29rbGWfTcSxQvtuLr1U+zd+9eRowYQWJiInEeEbSVlfP8\nyrdv6+cJPd9NFczTpk1j9+7d6PU3PwO2a9cuXF1diYuLu+F1jz32GGlpaaSlpeHicn1/RkEA+Oyz\nz7CwsCAkJAS9QU9AvwAKrugZK0lFJzOHwCRTR/xZWq2WoUOHUlhYyMiRIxkzZgxhTv/d+GfnArp2\nRljkIZNKOHRBrGMWbg8xZgud7r8n/BUqrYEfO2TkVDZR06JmsL8jc+fO5dNPP2X48OEEBARQUFDA\n6dMds55YEpCIt68/4fUHWbx4MZ9//jltbW1YFrRQ9HoRa15dgVotNlsLN++mCuaFCxfy8ccfExQU\nxF/+8hcuXPjlk3KSk5PZsWMHfn5+zJw5k0OHDv1iqxhB+DkGg4EnnniC1157jaqqKpxjnInyjiKt\nsJZxsnT0fUeDmZWpY/4suVxOQkICKpWKgwcPMnHiRLJPZGNvbk82GpDIsC47RryvA4cvitk64fYQ\nY7bQ6UpSwd6HgvYaZBIZ3tbGo6iP5Rr7Lw8NdGbs2LEolUqGDx/O0KFDsba27rCCGakU4ubxya6D\npKWlYWlpyYABA9BVaZDby+n75CwUiq61jE/o2m6qYE5KSmLLli1kZGTg5+fH2LFjGTp0KB988AEa\njeZnX/Pyyy9TWlpKYWEhn3zyCQkJCWzevPm2hhd6h+bmZoKDg2lubqauvg5pgJQwxzCqc0/iKalG\nETHF1BFvaO3atXz66ad4eXmRmprKnDlzCHMMI6shFzzjoOAICaGuZF9u5HJDm6njCj2AGLOFTmUw\nQOlJ8B5EUWMRXjZeKP67p+RYXg2+TpbknEohKCiI5uZmHnjgAfbs2cPWrVtZt25dx+Xq/wBTQi14\ncnIcFhYWpKens/LllVi4W6F1aiG3slkcYiLctJtew1xTU8PGjRtZv349/fv3Z9GiRWRkZDB27NiO\nzCcIWFtbExQUBEBQeBCOox0JdQyjT8VB9EgheIKJE96YtbU1o0aNYvr06VhYWDBs2DDCncLJrctF\n3Xc4lGWQ6G8BwLdillm4TcSYLXSahlJougxeAylsLLy64U+r03MivwbXunMkJiZy7NgxAgICUKlU\nfP7557i4uHTsLK+1K5bRU/jn0CoKcrIIDg6mT58+tF5sRlWWzYB+QWzatKnjPl/oUW6qYL7nnnsY\nMWIEra2t7Ny5kx07dnDffffxz3/+k+bm5l98/ejRo9m1a9dvDiv0Pjqdjri4OHx8fJBKpZQUlSCz\nlGGm82a0PpUapziwcv7lNzKxRYsW8a9//YuQkBDKysqQlcnQGrRccgkAg46A1kw87S3EOmbhthBj\nttCpSlMB0HvFUdxYfHXDX9blRpratfSx0KNUKq9uKvXy8mLSpEkUFxd3fLa4h0BVz5EtbzBnzhxa\nWlq4a9FdKOwbaKipIjU1teMzCD2C/GYueuSRR5g4ceI1j7W3t2Nubk5aWlqHBBMEgOPHj3Pq1CnU\najVSqZQxfxyDxlbD5dxiBklLqA3vHu2vli5dyp49e8jLy6O1tZX2F9vhd5ClkBIhVyIp+I7RIbPZ\nfrocjU6PQiYO4RRunRizhU5VchLkFly2dkalU+Fn5wfAycI6ABIGRvKOSsWKFSvYv38/S5cuRSKR\n4OPj0/HZ+o4Ep0D61h/FYDDQ1NREZGAke9/ai88fXuGlFYs6PoPQI9zUb+Xnnnvuusd+OIpSEDqS\nn58f8fHxZGVlIZfLaXBtoJ9zPyQXdwPgEDvVxAlvTnR0NIWFhSxYsACdTkd6ajrSK1Ky63PBZzDk\nH2FEkDPN7VrRXk74zcSYLXSq0lTwjCWvqQiAQPtAANIKa2k98A7l+RextLRk9+7dPPTQQzz22GMs\nX768c7JJJBA3jwjdefZ9/G9mzZqFZbslbYVtVGx9k68zizh9+jQ6nejLLNzYDWeYKyoqKCsro62t\njVOnTl1dHN/Y2Ehra2unBBR6r7a2NuRyOR4eHtjb2zNi9AjylHlEOkfiX72WYrNAfBz8TB3zplVX\nV9PY2Mj8+fPZsGEDblo3smqyjDMgB//BUDcDUgkcvVTNAD9HU8cVuiExZgudTqOCy2dgyBPk1+cD\n4G/nj8Fg4MSlyzRdSuXdd69cXRZ04sSJzm/nFj0bDq4g0TKbEatWER0djV6rx8xMz4Lp46gvL+Tj\njz9m1qxZnZtL6FZuWDB//fXXbNy4kdLS0mtO4bGxseGll17q8HBC77Z+/Xr+8Ic/MHjwYHQ6HcUV\nxUikEnwkrkToLnLK93E64YbebVNQUMD69euJiYnBy8uL5NeSCXwjEE30H1AAthXHiPTy4GhuNX8Y\nG2zquEI3JMZsodNdPg16DXgPJK8mBWcLZ+zM7SiobqG2XYJP30Ds7CzZsmULf/3rX1myZAlbtmz5\n2bsgHcbKCcLvgjOf8tRXdVy4cAHvkd74zhtI3mdujB1WxejRozsvj9At3bBgnjt3LnPnzuWLL75g\n2rRpnZVJEAAoLCxEp9ORlZWFVCpl7ttz2Zi9EbsLp5BKDFjGdK+fycTERJYsWUJKSgr19fVoNVoa\nchvIm2pNqNIe8g8zIvAp/nUkj0aVBlul6BEq/DpizBY6Xcl/N815DSQ//2MC7AIAOHg6F317KyGB\n/nyzdycZGRmMGzeOwsJCLC0tOz9n/ENwdhvLpkby/iYFdko7Tv5lFwrPJMY/+3s8PDw6P5PQrdyw\nYN68eTMPPPAAhYWFvPnmm9c9fzvOfheE/+X555/ngw8+oL6+ntmzZ3O+7jzBDsE4X9jLRYMPARHx\npo74q8jlcl577TXy8/MJCDD+Uqn8rJLs+TmE9h0Jed8y/K6/s/pwLil5NYyLcDdxYqG7EWO20OlK\nU8HBD4OVM/n1+UwOmAzAv958lbLDO1j41+fY+Z9tJCQkkJSUhLOziboa+QwBl1B8yrazc+dOCq0K\nWfLoElQFqfx+3gz0tW+Qm5vLK6+8gkQiMU1GoUu74aa/lpYWwHhwRFNT03V/BKGjHDhwgOzsbPz8\n/Ojbty919XWcrz5PpG1ffFrOkGEzBjN59+sk0djYyFNPPcWLL77Ifffdh1wp53DaYfAfDY2lxFrX\nYqGQkZxbbeqoQjckxmyhUxkMxg4ZXgOpbK2kWdOMv50/ACqXUPSqFvLycnn11Vc5duwYCxcupL7e\nRJuaJRJji7nyDMZHupH+VTqtOa1YO1pj4RXG4sWLWbt2LXl5eabJJ3R5N5xhfvzxxwH429/+1ilh\nBOEHTz75JK2trZSXl/PAAw+gsFVQrCkmrMXYQ7YpcLKJE94aGxsb8vPz2bNnD/b29jQ3NbPr/V28\n8+liAMyKjjDIP5rvRcEs3AIxZgudqqEEmiuM65cbjIVmgH0AVU3t1OqNyy42bNjArl27WLFiBR9/\n/DG2tramyxt9H3yzHNI/4EreFSQyCUMeHMXx72R88No/GDt8AA4ODqbLJ3RpNzVF96c//YnGxkY0\nGg2JiYk4OzuLI1OFDjVo0CCuXLmCXq+nT58+TF5kLJBDCjLI1PsTGBpl4oS3RiKRsH37dpYtW4aD\ngwMGrYH61nrarfuAvQ/kf8vwQGfyq1oorxfHZAu3RozZQqe4un55wDUdMl5885+AFHtHJ6RSKaNH\nj+bpp58mPT0dqdSEdwYtHKDfPXD2cx6f+yAKCwUlmRnUH97AO/9+j+3btwOI47KFn3VTP7n79+/H\n1taWXbt24eXlRU5ODq+//npHZxN6sVdffRWtVouNjQ3Tp0/nbPVZrOQWRFRlsUs3mFif7jsLEBQU\nxIoVK3B3d8fC2oK6Y3Vs/GIT+I+Bgu8ZEWD8fzt6ScwyC7dGjNlCpyhKBnNbcOtHXkMe9ub26Jp0\nvPP3P9OU8injx43D3Nz86nr6LrE2OP5hUDdzR596HvvkMSzjlICEtO+/4b333iMhIYEVK1aYOqXQ\nBd1UwazRaADYs2cPs2bNwtFR9IgVOkZ7ezszZszgz3/+M1FRUTg6OvLCCy9wtvos/WS2gITzDonY\nW5qZOupv8tBDD1FYWMjmLzdjEWDBlzu+NK5jbm8gWHcJFxtzsSxDuGVizBY6ReFR42Y6mZz8+nz8\n7fxxdXXFzieEltxUFi54nHnz5vH66693nWVCnnHgFokkfSNBdoGkvZyGRAJSt2BSUlJwcnLC3V1s\nuBaud1NHY0+ePJnQ0FAsLCxYu3YtVVVVKJXKjs4m9EL5+fkcOHAAtVpNUFAQL7zwAkorJS/Wvsjc\nVg3HicLXv/v3KB4zZgybNm3i9edfpy2/jeS6ZJpXvYs1EiT5RxgeOJbvcqrQ6w1IpV1gVkboVsSY\nLXS4pitQnQP9H8BgMJBbn8t4v/G0tGtpadcgkcqwt7fn9ddfp2/fvgwbNszUiY0kEoifB7v/SIzl\nQyi9lRjKpchsXXnkmeW88McFpuvkIXRpNzXD/Morr3D8+HHS0tJQKBRYWVldXesjCLdTWFgYcXFx\ntLe3k5mZiYuLC4HDAtEatEQ1VvOJegRxvt1/tmzu3Lns3LkTf39/MIBao2bPkRPgEQX5hxke6ExN\ni5rsikZTRxW6ITFmCx2u6Kjxb7/h1KhqaFQ3YtVgxbT7ZmMdPQGDXsfLL7+MlZUVzzzzDEOHDjVt\n3p+KnAEKK4ILU3C/1537/nAv2ssX+fSDd/H09CQ5OZnMzExTpxS6mJtefZ+dnc2nn37Khx9+yOef\nf87+/fs7MpfQC2m1WgwGA+PHjwcgICCAsLAwTlWeAiBCq2C/Pp543+67fvmnkpKS6NOnD979vJFY\nSVi4cCFq7xFQksoIXwtArGMWbp0Ys4UOVXgUzGzAPfrqhr8rmVc4sPM/aKoKCAwM4sCBA+zevRu9\nXm/isP+P0hZCJ+J28QB9IvrgOsQFZ0d7GirLsLa2ZsuWLcTGxlJRUWHqpEIXclNLMh588EHy8vKI\niYlBJpMBxsX7c+bM6dBwQu+ydu1aVq5cSXFxMU899RSrV6/mX//6F80J9fhptORajcZGb42vkwlO\nieoAR44c4Y033iDp3iTqLtShrFdySRJAhF6Da81JAl2tSc6r4fFRAaaOKnQzYswWOlzhUfAZDDL5\n1ZZy8jY5er0Oy/Y6UlKOs2DBAu69917Kysq6Xru28KlIzn5GiDKOrPIsrlzKRGbjgkanZtiwYYwY\nMQI7OztTpxS6kJsqmNPS0sjKyuoaO1yFHsvPz4+amhokEgnx8fEcOXIEjz4ezDs2kzEqFZtahxHv\n69hjfg6TkpKIjY2lprCGluwWpDZSWu1DQGEJuQcYFvAQ29JKUWv13fKQFsF0xJgtdKjmSuP65Zj7\nAcirz8NGYcOMu2fyyktvoq0rw87Oji1btnD69OmuVywDBCaBmTWhqlZOKSp59PHHWPfhNpqbmpDJ\nZNjZ2WFhYWHqlEIXclO/hfv16yduTQgdbsqUKZibm2NhYcGcOXPw8PBA4gD1OhVRZi7sb/Ai3q8L\nDry3SCaTsX//fl564SUMWgON9Y2sePlVMmXRcGk/QwOcaNPoOFVcZ+qoQjcjxmyhQxV8Z/zbbwRg\nLJjV36l5cN7DyBw8qS0v4syZM5iZmTFw4EATBr0BhRJC7iDiyiXUejWP/nk+D7y8FTNbF+bPn8+C\nBQt4//33KSoqMnVSoYu4qYK5urqa8PBwxo8fz5QpU67+uRGVSsXAgQOJjo4mIiKi67SUEbqkzMxM\nduzYwd13341arSY0NBRLS0syLnwGgLXzFEDCwL7df8PfTzk5OXHuzDk8+nsQ+UAk6enpZOv9oL6Y\noXa1SCWQnFdj6phCN3MrY7Yg3LTcg8ZDQPrEAJB+NJ2M9RmcP3MKpXc/PPp4snTpUvbt22fioL8g\n4m4imowTErktuQTIq1HXX6GtrY1x48Yxf/58vvrqKxOHFLqKm1qSsXz58l/9xubm5hw6dAhra2s0\nGg3Dhw/njjvuYPDgwb/6vYSeTavVMmHCBJqamnB2dmbt2rUsWLCA5uZmTuXtxVGn5yTjsTSrIdzD\nhMeqdpBt27bRkN9As7YZVZWKUr2xpZFNySEivWI5llvNkrHdv5We0HluZcxWqVSMHDmS9vZ2tFot\n06dP5+9///vtDyd0bwYD5B0y9o2XyqhX1aOyUeHh50FlaR2BI6fyn9+vYsqUKahUKlOnvbGARLyl\nFthK5JyrPsfvZzzNP5b5oKkpQaFQcO7cOcLDw02dUugibmqGedSoUfj5+aHRaBg1ahQDBgwgNjb2\nhq+RSCRYW1sDxib6Go1GrKcTfpZUKmXFihW0tLRgaWmJWq2msLCQIDcrMlSVxFp5cqxERayPA3JZ\nz1vLu2TJEkIiQmivaQcJDBw5jkabELi0n2EBTpwuqae5XWvqmEI3citj9g+THJmZmZw+fZp9+/aR\nkpLSSYmFbuPKeWiugIBEAC7VX0JuI2fclHFo29swZO2nb9++ZGZmdv27GgolkpAJRKhUnK8+h5Od\nNXf94TXsggby4Ycf8sc//pHy8nJTpxS6iJuqPt577z2mT5/O448/DkBZWRlTp079xdfpdDpiYmJw\ndXVl7NixDBo06LelFXokqVSKj48PYLyV/Je//AV3d3cqU/5JqUJOuO8ELlQ09qj1yz81c+ZMDh86\njK5Zh0at4bnnnmPqR1VQdJyRPuZo9QZSC8SyDOHm3cqYLSY5hJuSd8j4d0ACABs/2kjxv4vZ8dEu\nAFrKLqJWq5FKpUil3WCCI+Ju+rW1cKnuEiqtijl3jkAWMJjW1lYOHDjAX/7yF1atWmXqlEIXcFM/\nzWvWrCE5ORlbW+Pt8KCgICorK3/xdTKZjNOnT1NaWkpqairnzp277pp169YRHx9PfHw8VVVVvzK+\n0N01NDSwfPlynnnmGZYuXUpLSwshISHIdW1kZG0DwEwRj8EAA/x61vrlnzp++Dj6dj1jnhnD0KFD\nGTJ8BAadmljdaczkUpJzRcEs3LxbHbNvZpJDjNm9XN5BcAkDO0+am5tZ/7f1qIvV1NXWYpfwCEoZ\nJCYmmjrlzQtIJEInRYeei3UXGRvuhpWdcXLGwsKCK1eucP78eROHFLqCmyqYzc3NMTMzu/rfWq32\nV8082NvbM3r06J/dAPDYY4+RlpZGWloaLi4uN/2eQs9w+PBh/v73v5OTk8OAAQN45plnCA8PR5Kx\niVNSHRZSMyqqHJFJJfT3sTd13A4jlUqRaCWk7UjjjTfe4FReJRILB8xyvybe14HkXHGAiXDzbnXM\nvplJDjFm92LqVig6fnV22dramlErRqFp0OAWEIHfyOm8/spLPP300yYO+isolPTzHALAuaqzKBUy\nZtx9F9bBg5DL5fTv35/Vq1ebOKTQFdz0GuaXXnqJtrY2Dhw4wL333svkyZNv+Jqqqirq6+sBaGtr\n45tvviE0NPS3JxZ6lKlTp/Lwww+jUqlYuXIlra2tfPj+e3B8DadsnYhy7U96URP9+thiaXZTe1S7\npdGjRzN+1niwMM7yDR4ylL0tERgu7GGEvx0XKpqobm43dUyhm7iVMfunbjTJIfRiBd+Brh0CjTPI\neoOekvoS5GZyKvKyCVTUM2HCBO666y4TB/11XEOn4qzVcb7E2C7vnjgvHKc+h29IJKtXr+bhhx/u\neqcVCp3upgrmV155BRcXFyIjI3n33XeZOHEiL7zwwg1fc/nyZcaMGUNUVBQDBgxg7NixTJo06baE\nFnqOyspKrKyscHJy4uzZs5w4cQLObKO5uYKLEg1RLtGcLqnv0csxAMzMzFizeg1KfyUA6enpTHxh\nL+kFtYy1Nh47e1y0lxNu0q2M2WKSQ/hFF/cYj8P2G8Hu3buZcs8Uct7MwWAwILN1RVuQikajMXXK\nX00SPI5+ag3nqo13VAb3dcLT3oLLtY20trZy6NAh4uLiMBgMJk4qmNJNTdlJpVKmTp3K1KlTb/oW\nXFRUFKdOnfpN4YSe7Y033mDdunW0trby0ksv8fjjjzNl0iRIfpt0j1D0tOAoDUetVRHfwwtmAF8b\nXxq+a8DRz5F+/foRFhxIjPVmpDXfYqNM4lheNZOj+5g6ptAN3MqYffnyZebOnYtOp0Ov1zNjxgwx\nySH8SK+HnH0QlARyMyorK0k9kQo6CI7tT0m7M5dSD189ir1bsXAgwtKDI5o6mtXNWJtZc1d/T/4h\nNW6CbWtrY9CgQahUKnH6Xy92wxlmg8HA8uXLcXZ2JjQ0lJCQEFxcXPjHP/7RWfmEHqyuro66ujra\n2toYNmwYr732GvNHeELNJU54R2IuM6eq2h2gxx1Y8r/ItXJaVcYvEFs+2YY8OBHphT0M7usoNv4J\nv+i3jNk/THKcOXOGc+fO8de//rUTEgvdRvkpaL4CIRMBeOihh3ALdEPfrid45HS8Jy/i6JHD3aMz\nxs/o5z0CgwSy8r8GYHqcF/aj5jLqnjk0NDQQHx8viuVe7oY/2atWrSI5OZmTJ09SU1NDbW0tJ06c\nIDk5mbfeequzMgo91IsvvoiDgwO1tbXcddddVFdVYX92PTj05YS6hhjXGFLzmwj3sMXRyuyX37Cb\nk0ql/PntP+N0txNgbPP1ZpqElKxCprhWUlzbSkltq4lTCl2ZGLOFDnNxD0hkEJhEXV0dly9f5nyy\nsXvE0e2fE+vjgIO9nYlD3rrIyAcAOHNpJwABLtaMiI+kNWwScrmcxx57jOzsbLEsoxe7YcH84Ycf\nsnXrVvr27Xv1MX9/fzZv3syHH37Y4eGEnqu+vp63336bmJgY4uLiKCoqwkXeDGXp1A6cT079JeJc\nB5BeXMfQACdTx+00D9/9MObO5kilUqZMmcLy93awL1fPMPUxANEtQ7ghMWYLHebiXvAdil5pz4AB\nA1i8eDEGvQErF2tqC7OIdOnekxp2LmH46aVkVv/YGWb2IF/Ka1uQSCQYDAbCw8N/tnOM0DvcsGDW\naDQ4Oztf97iLi0u3XNgvdA0tLS14e3uzePFihg8fTktLCx4eHvwxtBysXDnpavxlb20IQ63VMyzw\n+p/BnsrLxgtlpRI9es6fP8+9985g+cPjcSjcjau1Gcli459wA2LMFjpETR5UnoeQO9BoNCxcuJB9\n+/Yht5Uz4qEJOIx5mJH9fEyd8jeLsunLGUMrhsbLAIyPcMPeXIJGb8DR0ZGYmBjc3d1NnFIwlRsW\nzD/t4/lrnhOEG9FqtSxevBilUsnq1atZuXIlx758D0n+YRi8kNTKU1gprCi/4oRcKmFAL1m//AN3\niTtSuZRvv/2Wbdu2oQmZgqSugPs8qzmeVy1uCQr/kxizhQ6R9ZXx77ApmJubk5+fT0trC0jBLWw4\njnF39Ig++dG+Y6iVySg9txUAc7mM+8cNxG/RVrx8fKmoqBBfPHuxGxbMmZmZ2NraXvfHxsaGs2fP\ndlZGoYexs7Nj0qRJqFQq8vPzufPOOzny4UvGdkXxD3Oi4gTxbvEcz6sn2tsea/Oe23/55yz43QIC\nXw7EzNyM5uZmlmxM4ZkDaibJUqhuVnPxSpOpIwpdlBizhQ5x/ivwjEdr7cGuXbs4ffo0CjMF2gYt\nhQUQ6WmHUtENu2P8P9EBEwA4nbv36mOzBvhgUFigs3CgoqKCwYMHU1hYaKKEgindsGDW6XQ0NjZe\n96epqUl8yxJuyZUrV/jTn/7EqlWrmDZtGmZmZri5OHOHMhPi5lKibaKosYj+LgM5U1rfq9Yv/yAh\nMAGFowKFhYL4+Hh0EjlNyj4EVB0ADKJbhvA/iTFbuO1q86HiDERM5ciRI0yePBmtVouqTYXEUkJx\ns2uPuQsYaB+IlUROZmMeqBoB8HO2YnigM5UaJRKJhJKSEl5//XUTJxVMoXv2fxG6rU2bNvH666+T\nnJzMhAkTGDx4MFufHoejpRQGLeBo2VEArHQR6A0wNKD3rF/+gZOFE77tvuhlekpLSzl48CBrXvsH\n8qYy7nQoFRv/BEHoPOf/uxwj/C5CQ0MZPXo0qamphE0MI+nfd6JX2DKohxTMMqmMfnaBnDFTQO43\nVx+/f5APkr6DGDxmHM7OzixZssSEKQVTEQWz0KmeeOIJli1bRklJCStXruR3j85juPoIREwFe2+O\nlh3F28abnFILzOXSHrEu7laMCR+D3lJPfX09BQUF7Mg10KY34wHLVE7k16DRiWNaBUHoBFlfgWcc\n2PuwatUqUlJS63UefwAAIABJREFUkMlkNBmasDL3RSKBOJ+eUTADRHkNJ8dMQWv2jquPJYW74Rs9\nFLOQkahUKqZPn05xcbEJUwqmIApmoVNptVrKysowMzOjurqaRx9bgKG9EQY/QbuundTLqQz3HM6x\nvGoG+Dn2iHVxt2Jc6DgC/x6IwkKBVqvlvU0f4/t2M1H136BWt3OmtN7UEQVB6OmqL8HlTIi4h+Tk\nZAB8fHzQ6XQ0NzbT2OBCRB9b7CwVJg56+8S49UcnkXC++Aho1QAoZFJmDfShwCKE5uZmTp8+zYMP\nPmjipEJnEwWz0GneeustPDw8sLKyQq1WU19fzxNDrDDrOxS84kivSEelUxHpMIgLFU0MDex965d/\nEOEUgYOFAz4DfDAYDAwZMoTH7r8bXWs9ibIMsY5ZEISOl/kJSKQQOZ1du3axevVqCgsLcXBywGO2\nB6VX7BjWw5bNRTlHAZAp1ULR0auPzx7kg8xMibWj8ah5sYm29xEFs9ApDAYDW7ZswdPTk1OnTrF+\n/Xry961laXw7DHkSgO/LvsdMakZTvbGf5+hgV1NGNimZVMbQPkMpyC7A3Nyc5cuX8+CTz2Lr5MFD\nlsfEOmZBEDqWXg9ntoH/GLBxx8bGBpVKRXBwMMs+XIbMUoa6zY2hPaxPvr3SHj8bHzItLODC7quP\nu9kqmdDPHddJf8RcqeTZZ59Fp9OZMKnQ2UTBLHQKiUTCyZMnCQwM5Pjx47zwwgtkfLkGKzd/CLkD\ngKNlRxngPoDk3CZcbcwJ87AxcWrTGuU1CvsEe9y9jI3yJ9w5iZPKEcS2p1FcXEibWgzWgiB0kOJj\n0FAM0TMpLi7mr3/9Kw4ODpw7d46soizMJNYoDHYM8HMwddLbLso1hjMWVhgu7IGf9L1/cLAfWvcI\nrGwdePrppwkJCUGlUpkwqdCZRMEsdIry8nIOHTrEiRMncHd3p6aqkvrSizDwMZDKKG0qpbCxkKF9\nhvF9ThWjgl2QSCSmjm1SI7xG4JroilahRS6XY2Njw8Dfb+B4iZqJfM/JwlpTRxQEoafK/AQUVhB6\nJ6+++ip33303dXV1uLu7o/JSIdF40N/HAUuzntcnP9olmlq0lLZdgfJTVx8f7O9IsJsNWoUVAPn5\n+eTk5JgqptDJRMEsdLiqqiqio6NJSkoiMjKSkJAQIn3suT/GCqJnAlxtJ+ckjaJRpWV0SO9djvED\nGzMbBrkPwuMeD/z8/JBKpbz33ntERMcyQ/4dyZeqTB1REISeSNMGWdshfAoGhSXp6enGo7Dlcja8\nv4HcxjyaGl0Y1sOWY/wg2iUagEzltcsyJBIJDw7xxWbyUnz6BiCXy2lsbDRVTKGTiYJZ6HA1NTVE\nRkYybNgwioqK2Pz+OpIflCKPmgaWxnZER8uO4mXtRXaxOTKphOFBPXMg/rUSfBIoOl9ETk4OmZmZ\n5ObmYjfoQUIkJVTknDB1PEEQeqKLe6G9EaLu46uvviI7OxuVSsX69euJHB5Jm7YVfbt7jy2YA+0D\nsVZYc8rZ55qCGeDu/p7YufShRSslMDCQ6upq8vLyTJRU6EyiYBY6XGhoKG+99RZpaWmUlpYyZMhg\n1K0NEDcPgFZNK8fLjzPaezRHcqrp722PnUXPaVP0W4zxHoPjaEcGTx6MVCrl1Vdf5dnPznO2Wkpc\n7W7qW9WmjigIQk+T+QnYeEDfkRQVFWFubg7Ahg0byKk1LkEw13sR7WVnypQdRiaVEe0aTbq5Aqqy\noebHgthGqeDuWE9USieys7O55557mDdvnunCCp1GFMxCh6qpqWHt2rUsXboUrVaLlZUVvjY6zNzD\nwGcwAMfKj6HWq4l1Hs7ZsgZGh7iYOHXX4WLpQlxwHCo348YSa2tr3vznWj4s9WGqNJnUiyUmTigI\nQo/SUAa5ByB6JrX1DSxduhS1Wo3BYGD9+vVk12aDQcJQ737IZT23hIh3iydPXUe9VAoX91zz3IOD\n/VCGjUIqk2EwGCgtLTVRSqEzddhPe0lJCWPGjCEsLIyIiAjefvvtjvoooQt75ZVXWLRoERUVFfz5\nz3/mnRV/5qURWoidC//d1He45DC2ZrbU13kBMKoXt5P7OYk+ibSGtjJl2hRsbW156623eHHlamwl\nrbRkfGrqeEIPIcZsAYBTm8Ggh9i5pKenYzAYMDMz4+mnnyY4OJi08vPo1C6MC/c2ddIOFesaC0CG\ne/B1yzJC3G0YOX4y4bOfx93dnWeeecYUEYVO1mEFs1wuZ+XKlWRnZ5OSksKaNWvIysrqqI8TuqgZ\nM2awbNkyzp49y0cffcRE92pG9lVC5L0AaPVavi35ltHeo/kupxZnazMi+tiaOHXXkuCdgMxaxs6v\ndlJeXs6aNWv4NreVEkVf+pVtu6btkSDcKjFmC+h1kPEhBCSAY1+WLFmCXq/H2tqaqVOnAnCh7gJ6\nlQdjevidwH7O/TCTmpHu7AMlJ6D52k3WM+K9KSstoaa2jm3btrFgwQKxAbCH67CC2cPDg9hY4zc0\nGxsbwsLCKCsr66iPE7qo+Ph4vvrqK/R6PSUlJRzf+wkEjgVr42CbcSWDRnUjIzxH8e3FShJCXZFK\ne3c7uf/Pz86PYLdgEp5LoE+fPly4cIFFixfzToE/QfoCqi4kmzqi0AOIMVsg9xtoLIW4eVRUVBAW\nFoZGo6GqqgonJyca2hto0VXjYRGAk7W5qdN2KDOZGZEukWRI1MYZ95x91zw/KboPli5eaNTtfPfd\nd7z77rt88803JkordIZOWYBUWFjIqVOnGDRoUGd8nNBFfPzxx4SEhHDmzBmioqKQy2UMcmq82koO\njMsxzGXmmKvDaFJpSQpzM2HirivBJ4Fyx3IMGPD29qa8vJyCZnOaDBa0HP23qeMJPYwYs3uptA/A\nyhVCJrJy5Uo+++wzAJYsWUJQUBDHS4zHQQ/2ijRlyk4T6xpLdlMRrXbXd8uwNpdz79RJ2EWPw/Df\nu3xSac9d0y10QsHc3NzMtGnTWLVqFba2199qX7duHfHx8cTHx1NVJfrK9hStra088sgjtLS0MGvW\nLLZv387p16fi5ux49WQ/g8HAoeJDDPYYzHc5jZjLpaKd3P+Q6JOIxEZCbFIsNTU1TJ48mc+2fsw+\n2Wg8y/ZBS42pIwo9hBize6mGMrj0NfR/AJVGx5o1awB4/PHHee655wDYm5MBwD0RA0wWszPFu8Wj\nM+g47T8A8g+DuuWa52cN9sd62Gzcvf14/vnnSUpKQq/Xmyit0NE6tGDWaDRMmzaN+++/n3vuuedn\nr3nsscdIS0sjLS0NF5eevSaqN7G0tOTixYtYWFiwdetWnnryd0Q0H4V+00BuvJWXU5dDeUs5Y7zH\n8E32FYYHOvfIU6Nuh3CncNws3aiR19DW1sYXX3zBoEGDKA2chQIN2vQPTR1R6AHEmN2LXd3sN4cL\nFy7Q1taGvb093333HXK5cVw+feU8Ep0t8d4+Jg7bOaJdo5FKpKTbOoFWBXmHrnl+gJ8Dfq6ONDS3\n8eGHHxIcHMyECRNMlFboaB1WMBsMBubPn09YWBhLlizpqI8Ruqi2tjaeffZZ8vPzkcvlWKhrQNsG\n0bOuXnOo+BASJHibx1NS20ZSuFiO8b9IJBISfRLRjNEwbMQw9Ho9WVlZbFj5Esd14WhPrDdu2BGE\nWyTG7F7s/232O3LkCBKJhPr6embPno1EIqGqqZ1qdSEeFv5IJL1jn4mVwoowxzDSVZWgtIcL17aX\nk0gkzBgaSLuqjaKiIioqKjh9+rSYZe6hOqxgTk5O5qOPPuLQoUPExMQQExPDnj17fvmFQreXm5tL\nQkICH3/8MRMnTmTQoEEsGiAFR3/w+vFW3qGSQ8S4xnAyXwNAYqhoJ3cjY33H0q5rp/+4/jzwwAO0\ntLTg7mjHJt1YlC2lkL3T1BGFbkyM2b3YTzb7JScns3z5cmQyGTNnzry6HGN7ZhES8ysM9uwd65d/\nMNBjIJnVZ2gNGgs5e0Gnveb5+wb1xXvBesIGjUEqlTJ8+HCxlrmH6rD738OHD7+6EF7oXbKyssjO\nzsbb2xtLS0u+/OBtFGtiIfrZq72Xy5vLuVB7gT/G/ZGvjlwh2tseV1uliZN3bf1d++Ns4Yymn4YP\nnv8AiUTCs8uWsjHPnLKyT/E8vhoippo6ptBNiTG7F/vJZr/Xp91LS0sLPj4+vPbaa1cv+fzsKSSW\nOgZ7966CeYjHED449wFpHiGMPPsZFB+HviOuPu9mq2RMpC87vjHg7u7OnDlzSE1NJSIiAisrKxMm\nF2438TVIuO2SkpKYP38+hYWFfPbZZ5QeWm98Iuq+q9ccLjlsfMhpKKdL6kkSs8u/SCaVkeSTRFpT\nGvfNvA+lUklCQgJW5Rn8Wz0BSk9CSaqpYwqC0J38ZLMfMgUqlQqNRkN+fj4nT54EoKC6hdz6iwCE\nOIaYMm2ni3WLxVxmznFJO8jMrzv1D2B6nDdqiRktbSruvvtuBg0axPr1602QVuhIomAWbiutVsvS\npUt58803kUqlREVF0bdyP/gOBwffq9cdKDpAoH0gOSXGWWWxfvnmjPMbh0qnwn+oP21tbVhaWvKv\nv/2erXVhtMtt4dg/TR1REITu5Ceb/c6dO8ehQ4eQyWQ89NBDTJ48GYDtp8uQKS9jLjPH18b3F96w\nZzGXmRPrGktKZToEjIELu647LCoxzBV7/ygsXXzEcoweTPzLCrfVo48+yrp16wgNDSUlJYWtby6D\nmlyI/nF2ubqtmowrGYz1Hcs32VfwtLcg1N3GhKm7j1jXWJyUTrSEtLBmzRqsrKwIDQ3F06MPX1tM\nNA7mtQWmjikIQneg18Gpj8B/NBVqCxISEtBoNDz66KNs2LABhUKBTm/g8/RSHOyrCHYIRiaVmTp1\npxvSZwi59blU+o+E+mK4cv6a55UKGfPmzsVi8nP4+vUlJiaGadOmmSit0FFEwSzcVnFxcQQGBnLx\n4kW+/PJLwluPg9wCwn9cW3uo+BAGDAz3GMP3l6oZG+7Wa3Zd/1YyqYwk3ySOVR7DP8ifqqoqSkpK\ncKjM4NXaERgkMjghDjIRBOEm5B2GhhKInUtNTQ06nQ53d3fMzMyuXnLoQiWlda3oFeW9bjnGD4b2\nGQpAsrU1ILnuEBOA6XFeaCRy6puasbS0ZOHChdesARe6P1EwC7dVUVERWVlZxs1DOi2c+w+ETwHl\njwcgHCw+iI+ND2WV9rRr9eJ0v19prO9Y2rRtyIJl3HXXXbS0tHDgg5XkX26gxHMiZHwErbWmjikI\nQleXsREsnSD0Tt566y1qa2upqKggJyfn6iTGpmOFuDuqaNM1EeoQatq8JhLsEIyHlQeHKtPAe6Dx\nTt7/E+Vlh5eskbrqSvLz89m1axfPP/887e3tJkgsdARRMAu3zebNm1m1ahWurq7Mnj2b56dHQ3sD\nxMy+ek1DewOpl1NJ8k3i6/MVOFgqGOTvaMLU3U+cWxyOSkf2F+7HwsICf39/WluaaTu2mU2SKaBp\nEbPMgiDcWHMlXNwL0bPIOHOeTZs2YW5uzuLFi9m1y1gQ5lY2cTS3muERKgBCnXpnwSyRSBjjPYaU\n8hTagsdDxRmoL7numrl3DMFx7EJiBw0DwNzcXKxp7kHEv6RwW1y8eJEHH3wQiUTC22+/zebNm7G4\n8AXYeoHfyKvXfVvyLVqDllFeCXyTXcm4cHcUMvFj+GvIpXISfRI5UnqEf6//N4MHDwYgbtAwPi6w\nRhcyGVL+DW31Jk4qCEKXdfpj0Gsx9H+QmTNnotVqGTp0KG+99RYymXGd8qZjRZjJpbg4VSKXyAlx\n6J1LMgASfBJQ6VQcc3Q3PvAz3TKmxnhiH3cnfQZOxNramhUrViCTydDpxKFSPYGoVITbwsPDg2HD\nhqHRaLj//vvR1ZVA/mGImQU/+Yb9TdE3uFu5U1vjRnO7lgmR7iZM3X2N8xtHm7aNk9UnmTNnDhKJ\nhO+2vkNdwVlO+Mw3zuynrjN1TEEQuiKDwXiyn88QKg0OREYaeysfOXKEb7/9FoDq5nY+Sy9hSnQf\n8psuEugQiFLee3vlx7rFYmNmw+G6bHAO+dl1zK62SkYFu3CsuBVPTy+WLl2KtbU17777rgkSC7eb\nKJiF2+LJJ58kOTkZmUzGnDlzkJ//3Niq6CdHYbdoWjhWfowknyT2nruCjVLOsABnE6buvuLd4nFU\nOrK3YC9BQUGYm5uj02qp2/0mn5XYQ8hEOL4G2ptMHVUQhK6mKBlq8yB2LlOnTuXLL78EYODAgQwZ\nMgSA977PR63Vs2CUP+drzhPhFGHKxCankCoY5TWKwyWHUYdMgMKj0FZ33XXT47y4fCmT8ooKLCws\naGtrY+vWrSZILNxuomAWfrN9+/bx2WefERkZSUpKChvWrzfe7vMZAk4BV6/7vvR71Ho1o70SOZBV\nwdhwN8zk4kfwVsilcsb7jedI6RGcPZ353e9+h4+PD+r6CvaknEMz7GlQ1UPqe6aOKghCV5O+Cczt\nOKPzJycnB4VCwdmzZ9m7dy/m5ubUtqj56HgRk6P7YG5RT0N7AxHOvbtgBpjYdyKN6ka+d/IEgw5y\n9l93TWKYK56DJzNr5Q5iYmKQy+UkJiaaIK1wu4lqRfjNNm7ciF6vp6qqCjs7OyhNg5pL12z2A+Nh\nJU5KJ1qbvGhUabmjn4eJEvcMk/wn0a5r52DxQVauXImTkxMAZQc3cVzlA4Fj4fhqaG82cVJBELqM\n1lrI2g5R97L/8Pc0NTURGhqKTqfD3t4egA1H82nT6HhyTCDna4w9h3v7DDMY+zE7KZ3YWZ8F1u5w\n8fplGeZyGXcP9OdwQTPLX3wVgObmZl5++eXOjivcZqJgFn6TEydOsG3bNjQaDRUVFbS2tkL6B6Cw\nuqb3skqr4vuy70n0SeTrc5VYmckYESSWY/wWkc6R+Nj4sDvfOGgvW7YMuVxOy7mD/Gvrdhj1Z2it\ngZS1Jk4qCEKXcWYb6Nr5KN+JDRs2YDAYOHPmDJs3bwaMa5c3JhcysZ8HQW42ZFVnoZAqCLIPMnFw\n05NL5dzpfydHyr6jPigJLn0DGtV1102P80Kt1fP0s39DqVTyzjvvsGzZMlJSUkyQWrhdRMEs/CZP\nP/00BoOBAQMG8OmnnxId6AVnPzee7PeT3svfl31Pm7aN0V6JfH2+gsQwN5SK3ndi1O0kkUiY5D+J\n1IpUKloq0Ov1aLVaQMIX//w77R6xEDYFjq6CpiumjisIgqkZDJCxCfr0550Pv+TChQv079+fmTNn\n8txzzwHwz4OXUGn1/GFsMADnas4R6hiKQqYwZfIuY3LAZLR6LXscnI0tPAu+u+6aSE87gt2s0XrH\n88ADD/x3XDZ2kxK6L1EwC7esoKCAlJQUBg4cSEpKCjNmzDAes6prhwGPXnPt3oK9xuUYjX7UtWqY\n2r+PiVL3LHf634kBA3sL9jJ9+nRycnKwsLJEU1PKBzu/g6Tlxn+Pwy+aOqogCKZWlg6VWRS4TeTU\nqVPIZDIOHDjA1q1bsbOzo6C6hS0nipk5wJtAV2v0Bj1ZNVmEO4WbOnmXEeIQQj+nfnxSk4HBzAYu\n7LzuGolEwuyBPtS4D+TxZS/z6KOPIpVKUSqVosVcNyYKZuGW1NXVMWvWLKytrUlNTWXhwoWg10Ha\nBvAdDm4/DrBN6iaOlBxhvN94dmRW4GhlxoggFxOm7zl8bH2Ico5iV/4uJBIJgYGB9PX1BYmU55f8\nDq2dr/HLy6mP4Mp5U8cVBMGU0jdyWWXOkSs2hIaGIpfLmT9//tWn3/j6ImZyKYuSjMsvihqLaNG0\niPXLPyGRSJgdNpuCxkKOBwyBrB2gvf40v2lxXliZydh0rJBRo0bh4uLCq6++ire3t/EkXKHbEQWz\ncEs2bNjAyZMnqa+vx9zcnKeeegouHYD6Yhj4yDXXHio+hFqvZpTnOL7JusKkKA9xWMltdKf/neTU\n5XCx9iISiYR+/fqBQU/t5RJ27/8GRv0JlPawc5HxS40gCL1PexOc+w9/PGbP/IVPcvHiRdrb2xk+\nfDgAJ/Jr2H32Mo+O8MfVxthv+eqGP9Eh4xrj/cbjpHTiYwupsRvRpQPXXWOjVHBvvDe7zpTz/fFU\n6urqOHv2LJcvX6aystIEqYXfSlQtwq926dIlnnnmGdzc3Pjiiy9QqVSEh4fDsX+CrSeETrrm+j0F\ne/C09qTksgvtWj1T+3uaKHnPNKHvBORSOV/lfgXA3/72N8KiYtC3tzDjnntQy61hwitQehJObjBx\nWkEQTOLs56BpobTdEr1ez5o1a/j+++9ZvHgxWp2ev+04j6e9BQtG/dgK9GzVWSzkFvjb+ZsweNdj\nJjNjRsgMjtRlkWvrCmc+/dnr5gzxRaMzEDTxUbKzs5HJZMjlci5dutTJiYXbQRTMwq9WWlqKl5cX\n1dXVSH84xa/4BBQdhSFPwk82h1S1VnHi8gnu6HsHX6SX4edkSX9vexMl75kclY4k+iSyI28H7bp2\nwsPDObx/HzJzS9TtbTz77LMQNQMCEuHg36G+xNSRBUHobOkbKTcLJDXzApaWlgQEBFydXd6cUsSF\niiaeuzMMC7MfN2NnVGYQ5RKFXCo3Veoua3bobCzllrzbpy/k7IO2+uuu8XexZmSwC1szLtPH25cj\nR44glUrZu3cvq1evNkFq4bfosIL54YcfxtXV1Xh7WOgxzp49S0JCAhUVFWg0GrZs2WJ84uibYOEI\ncXOvuX573nZ0Bh0x9kmkFtYyc6APEonEBMl7tunB02lUN3KgyHhr0NXVFbc+XiBTsGrVKkrLymDS\nW8Zd8v95DHRaEycWuiIxbvdQ5afYuv8kCevK0Ov1tLa2Xj2uubq5nZUHchgR5MyEfu5XX9KkbiKn\nLodY11hTpe7S7JX2zA6bzdftFeRJ9cbe1j9jwSh/qpra2ZZWQlVVFWq1mldeeYVFixahVqs7ObXw\nW3RYwTxv3jz27dvXUW8vmEBpaSkTJkwAICYmhhdffJFPPvkEKs4Zv2EPXghmVlev1xv0fJ7zOQPc\nB3D4HChkEqbHeZkqfo820H0g3jbefJ7zOWDcmJIwfCjodWi1WuPGHgdfmLwKio/B4RdMnFjoisS4\n3UOlb2TnJT0Xi64QGRnJpEmTrvZdfm3fBdrUOv42OeKayYzMqkz0Bj2xbqJg/l/mhM9BKVfyrpu3\nsV3fzxji78QAPwf+9W0eYyfcwbJly9Dr9ej1ekpLSzs5sfBbdFjBPHLkSBwdHTvq7QUTUKvVODk5\nERoayrZt21i2bBkymQy+ex3MrGHgta3kTlw+QVlzGXf538N/MkoZH+GOs7W5idL3bFKJlGlB00i/\nkk5+fT4A729Yx/w1e0GqYP/+/Wzfvt24NCN2Lhx9Cy6Kwki4lhi3e6D2JqpSPuXLbONdpY0bN7Jz\n507MzMw4WVjLtrRS5g/vS6Cr9TUvy7iSgUwiI8o5yhSpuwUHpQMzQ2eyT6EjvzLT2Lbv/5FIJPw+\nIYjLDSq+SC/jxRdf5MknnwTgkUceERsAuxGxhlm4KXq9nmnTplFaWsqFCxdYvny58YnSdMj6yrh2\n2cLhmtd8cekL7MztaKkNo1GlZfYgn84P3ovcHXQ3ZlIztmQbl8koFAoSfM1Br8HS2pa5c+fS1NQE\nd7wK7lHwxXy4fMbEqQVB6EhF+//NB6l1yBTGvSXNzc0AtKl1/OnzM3g5WPBU4vWn+GVUZhDmGIal\nwrJT83Y38yLmoZRb8G9HJ0hd/7PXjAhyJtrbnjWHc1FpdLz00ku4urry7bffEhgYiEaj6eTUwq0w\necG8bt064uPjiY+Pp6qqytRxhJ/R1NTEokWLOHfuHAaDAScnJ2PBbDDAgb+ClQsMffKa15Q3l3Ow\n6CCT/aew4WgJoe42DPF3Ms3/QC/hqHRkUsAkduTtoF5l3IBy16h4FJY2qCVyWlpaePnll0FhAbM/\nBaUdfDwDGsRtQeHmiTG7e1m24nX+8o2ado2WPn360L9/fwDePHCR/2PvvsOjLNYGDv+2JZseUkgC\nqfQUQiChl9CliTSVIgiKgIpigSN6PMLBo/ghRwFBEEW6gII0QTqB0Am9BQIkQHojve7ufH/sYTUS\ngigkC5n7unJB3vrMZPPsZHZm3tj0fGYMDMbGsuykvhJ9CefSzsnhGH+Ck9aJYf7D+NXaksuXN0J+\nxl3HKBQKJnVvSEJWIYsPxmFra0uPHj1QKBTk5uZy8+bNKohcelBV3mAeM2YMUVFRREVF4eoqH2Zh\njnbu3MncuXMJDg5myZIlpKen4+fnB1e2G1fGCH8PLO3KnPP9+e9BAb6aHlxLy+fVjnXlZL9KMMx/\nGEX6ItbGGMcy29jYMO7df+IQ/jI6nY4ZM2awc+dOsK8FQ3+E4jxY+SwU3q7iyKXHhczZj4+rketZ\nfzINASxfvpyrV6+i1Wo5efM2iw7EMrSlN23qudx1XlRKFCWGElp6tKz8oB9DIwNHYqu24mt7K4j6\nvtxj2tV3oau/G/P2XiUtr5ilS5cyYMAAVCoVH3/8sXE1I8msVXmDWTJ/UVFRuLm5cfLkSXS6/62u\noCuBHR+CUx0IHVnm+NSCVNbHrKdf3X6sOpSLl5MVvRt7VH7g1VCDGg1o6dGSVdGrKNUbP+abNfUf\n+NWti0prg6WlJSNHjuTSpUvgHgSDV0B6DKwaCqWFVRy9JEkPS1FREavmTqVQD95etRk0aBBWVlYU\nleqZ9NMZ3O21vN+zUbnn7o/fj6XKkubuzSs56seTg6UDI4JGscfGmgtRX0NRdrnH/bO3P8U6Pf/d\nfgWApUuX0rBhQ3755Re+/vpriovvfmKgZD4eWYN5yJAhtG7dmsuXL+Pp6cmiRfKBCY8bnU7Hvn37\nmD59Ordv30apVBIaGmrceWgOZMRAzxll1l0GWHJhCXqhJ8i2H6dvZTGmfR3U8sl+lebFgBdJLUjl\nl+u/AKBUKnitd0sUWjsCw9qSmJjISy+9ZDy4TkcY8A3cPAzrRssnAVZzMm8/OV4ePoSP1xrnKLi4\nuhknaAM/cZSPAAAgAElEQVTTt17iWlo+0wcGY6fV3HWeEIJ9t/bR0qMlVmqrSo35cTbcfzgOGlu+\nslbB4a/LPcbPxYaRbXz58cQtjsdlYm1tzfPPP092djZZWVm/LdMqmaVH1opZtWoVSUlJlJaWEh8f\nX+Z59dLjYcGCBXTp0gW1Ws3AgQNJT0/H19cXbscZV8bw7wv1u5U550bODVZHr6Z3nT4s3J2Nt5M1\nzzX3qpL4q6t2tdvh7+TPd+e+Q2cwfiIwpEMAWitrki1rY2VlxbFjx35bOD9ooPFJgNG/wJZ3jGPT\npWpJ5u0nw/jx49mzeyelBpg6+W0iIyNRKBRsO5/E0sM3GN3Oj/AG5Q+nic2JJT4vng61O1Ry1I83\nWwtbXgp+hYPWVpw8+Q0UZJZ73FtdG1Db0Yp/rD1LYYmeDz/8kPfeew+ADRs28NJLL5GRcfc4aKnq\nyW4/qVwFBQXo9XrUajV2dnZ88skn1KhRw9iY2joJFCroMb3MOQZh4JMjn2ChssBXMYjLKblM7tkI\nS7XqHneRHgWFQsHY4LHczL3J9rjtAGgtLfhxyy4UTZ7BycO4Wsknn3zCt99+azyp1Tho9zacWAIR\nn1VR5JIk/V0Gg4GVK1eQejufGtYa3vng31hbW3Mrs4BJa8/SxNOBf/QofygGwP5b+wHo4CkbzA9q\ncMPBOFs48JWtBWL3x+UeY2OpZsbAYGLT8/nvjssolUqmTJlC48aNOXv2LCtWrJBroZsp2WCW7iKE\n4NNPP+Wtt96iuLiYvLy83yb3nP4BYnZA5w/BoexDSFZeWsnhpMOMa/wm3+xNJ9SnBj1/9+QoqfJ0\n8u5EPcd6LDy7EP3/hln0CPGllY8Dqbdz8KtTl+TkZCZMmEBCQoLxpC5TIOQF2PfZPSeuSJJkvoqK\nimjfvj1ZWdkYgM/+/T52dnaU6AyMX3UKgLlDm2Ghvvdb/44bO2jk1AgPWznv5EFZa6x5JeRVorSW\nHL2wEm4cLve4NvVceKGVN4sOxnLwajoajYYFCxaQkJBAaWkp48ePx2AwVHL00v3IBrN0l0WLFrFv\n3z7UajVjx44lKysLW1tb4/Jj2yaDT1toOa7MOZHxkfw36r909OrIqfONyCooYdozgXJljCqiVCgZ\n12Qc17Ovm8YyKxQK/m9wC6w8A0lITadnz54UFhYyYMAA42QThQKeng31n4ItEyF2fxWXQpKkPysq\nKorQ0FBOnDiBrQWsn9iRMRP/DcAnWy5y5lYWMwYG4+V073WVr2Vd41z6OZ6u83Rlhf3EGdRgEG7W\nNfnK1Q2xaTyUFpV73Ae9/KnrasuE1adJzS2iTZs2xhWMgJycHDZt2sSePXsqM3TpPmSDWTLR6XRM\nnTqVhQsXcujQITp16sT48eOxtrYGgwE2vm6cFPbMPFD+9tLZeWMnE/ZOoEGNBnR1eZuNZ5IY37ke\ngbUcqrA0Unef7gQ6BzLv9DyK9cbZ174uNnwyczbOw/6Lu38YAMeOHeOjjz4ynqRSw6BF4FwPfhop\n12iWpMfE559/zsWLF7HRKNCqFfSaMAuAH4/fYunhG7zS3o+e91mtaM3lNaiVanrV6VUZIT+RLFWW\njG0yjrNqiCyIh63vljsvxNpCzbyhzcgrLuXNVafQ6Q107NiRf/3rX4DxKYDDhw+nsFCuXmQuZINZ\nMjlx4gT/+c9/OHnyJAaDgdTUVAIDA407D86C6xHw1Cfg5AdAZlEmUw9N5Z2Id/B39mdK2Gw+Wn+V\nwFr2vN6pXtUVRAKMPcpvh75NUn4Sq6NXm7aP69KI5kEN2BWvQKPRYG9vz4wZM+jSpQt6vd64pvbg\nlcalA9cMv2cPiSRJVU+n0zFz5kz27duHQqFAqS9i8ZtdsfBswsmbt/lww3na13fhvQrGLYMxn6+P\nWU+fOn1wsbp7bWbpz+tXrx+etp585dUAw6kVcOzbco9r6G7Hf/o15sj1TD7dGg3AlClT6NOnD7dv\n3yYxMZEWLVpUZuhSBWSDWTLZtWsX/fv3x9ramnXr1rFp0ybjkIobh2HPfyCwP4SOpFRfyrILy+jz\ncx82Xt3IiIARzOv0Le+uiUEIwdfDmqGRy8iZhZYeLWlTqw0Lzy4ks8g4a1utUjJ3aDNq+LfCyr0u\nBoMBDw8P9uzZw1dffWU80aU+9F8AiSdh68QqLIEkSfdy/Phx/Pz8WLJkCSkpKTT1cWDnKGf6TF5M\nSk4R45afwN1By1dDmt53ac85J+egM+h4KeilSor+yaVRang15FWiS7PYWa+NcSjjxU3lHjso1JOR\nbXz5/mAsq47dRKVS8cMPP9C9e3cUCgXW1tYsW7ZMjmk2A7JVU80VFBTQr18/XnzxRT788EP279+P\nu7s7LVq0wNvbG/JSYd3L4OgNT8/haPIxBmwawOdRnxPsGsy6vut4u9m7TPzxIpdTcpkzpCk+zjZV\nXSzpd/7R/B8UlBYw5+Qc07bajlbMGhyK43Of0P+zdaYH0kybNo3c3FyEEODfB9pPhFPL4eTyqgpf\nkqRyGAwGPvroIxISErh27RpODraEu+cTMvRfFFm7M3b5CfKKdXw7IgxHa4sKr7UtbhvrYtbxQsAL\n+Dn4VVIJnmy9/Xrj5+DH1zZq9LWbwdpRcHFjucd+2NufDg1c+deG80TGpGFjY8P69eupU6cOcXFx\nvPjii/j6+jJx4kTjp4BSlZAN5mquqKiImJgYNmzYgEKhIDU1lWnTpuHp6Wn8KH71MCjIJH/AAv4Z\n9X+M3jEavdAzr8s85nedj6+9H/9Yd5Zdl1KY+nQgHRvWrOoiSX9Q17Euw/yH8XPMz5xLO2fa3qlR\nTab0a8r+W6X4hHVFq9VSVFRE37596dChA/n5+dDpA+PDTbZOhKSzVVYGSZKMDAYDmzdv5rXXXuPA\ngQM4OTlRVFREN194pmVdRMtX+XDDeU7fyuKL50Jo6G53z2ul5Kcw7/Q8Ju+fTIhrCG80faPyCvKE\nUylVvBbyGtdz4tjabizUDoWfRsHRb+4a02z81K8p9WraMnb5CU7dvI1Wq2Xjxo1oNBoUCgW3bt1i\n+/btKJWy2VZVZM1XU9nZ2RgMBvbu3Ut4eDiWlpZMmjSJDRs28Nxzzxl/oTe/CfHHuN7zPww58Sm/\nXP+FVxq/ws99f6aDZwf0BsGktWf5+WQC73RrwIttfKu6WNI9vBryKi5WLkw7Ms30yGyAl9r5MaZD\nHRI82lFcXIK3tzfHjh3j8OHD/Pjjj6BUwcBFYOUEP46AwqwqLIUkSd988w19+/bl1KlT5OXlUatW\nLWa90ITVA7WEv7eGJUcTWHsinje71KfHH5b1vHL7CrNOzGL0jtF0WN2Brmu7suDMArr7dGdBtwVY\nqCruiZYeTHef7jSs0ZD5FxdTOvRHaPAU/PoP2DwBSstO5rPXalj2UgtcbC0ZteQ40ck5BAYGcuTI\nEfr164dWq6VFixZ88MEH7Nq1i9dee43U1NQqKln1JBvM1VBOTg7NmzenVatWDBo0iPnz51OrVi0M\nBgPPPPMMSoUCtn8AZ9dwsvUrDLu8iOzibL7t9i1vNnsTrVpLUamecStOsu5kPO90a8AbneUkP3Nm\no7Hhn63+SXRmNAvPLSyzb3KPRgzq2hr3UXN45o1/U1BQgMFgYNGiRZSWlpJRpIBnl0D2LeNKKfJJ\ngJJU6fR6PWvWrOHbb79Fo9Fw7Ngx+vfvT25aPM84X4OnPuVQfi3+s+US3QLceKtLfdO5N3NuMmbH\nGAZuGsjSi0vJK8mjk3cnJoVNYsMzG5gRPgMbjRxK97ApFUrGNx3PrdxbbLq1G55fCe3egZNLYWEn\nSLlQ5via9lpWvNwSrVrF4IVHOBufhaenJ8uWLSMoKIh169bx+eef061bNxYvXkxycnIVlax6kg3m\nasje3p4BAwZw8+ZNtFotdnZ2eHp6MmPGDGNjaNcUOPI1B0MGMTZtHy5WLqzuvZoWHsbZuhl5xYz4\n/hi7LqUw7ZlA3uxSX663/Bjo4t2FPnX68O3Zb7mQ8VuiVioV/Pe5JvTr3IrVN6xo1/s5FAoFZ86c\noV69etStW5cUS1/o9rHx8dmHvqq6QkhSNbR27VqaNGnC119/TXR0NBYWFlhZWdG0lgXNnXJxb96P\nqz7PM27FCeq42PDFc01QKo05eX3MegZsGsC59HO8E/oOe5/dy+o+q/l3m38zInAEdR3rVnHpnmzh\nnuEEuwQz/8x8Cg3F0HUKvLAOCjKMjeYj843Ltv6Pt7M1P45tja2lmmHfHuXQtXRsbW3ZuHEjnp6e\npsl/gwcPRqvVAjB37lyioqKqpHzViWwwVxNCCGbNmsWqVato06YNhw4dQqfTERYWxr59+/juu+9Q\nGHSw5R04OJtdjfswPvckvg6+LOmxxPTUpzO3snj6qwOcvpXF7MEhjGjtW7UFkx7I5BaTcdY6M2nf\nJHJKckzbNSolswc3pU+IJyei41CqNXTr1o3k5GSys7Pp2bMntHoVAp6BXVPh+r6qK4QkVRN6vZ7v\nv/+ec+fOcf36dQ4fPkz9+vUZN24cUT/P5V81d/HjxG7k9prLyCVRWKiVfD+yOXZaDaWGUqYfnc5H\nhz6iac2mbOy3kVFBo3DUOlZ1saqVO8t7phSksOT8EuPGel3h1UPG+SHbJsOSXpAeYzrH29man8a1\nxs1By/BFx1h2OA4PDw/Onj3LtWvX8PLyYv369QQEBNCiRQs+/fRTFi1aVAWlq2aEGQkNDa3qEJ5Y\nycnJwsnJSdSpU0cAQqFQiPDwcLFz507jAfkZQiztK8QUe7Fhw4sieGmwGLZlmMguzhZCCKHXG8SS\ng7Gi/gdbRZvpu8W5+KwqLI30d5xKOSVCloaI13e9LvQGfZl9pTq9eGXhHuH+4iwxaek+0axZM1G/\nfn3RunVr8d1334nWLVuI6A8bC/GplxApF6uoBOapOuav6ljmynLu3DkxYMAAYWVlJWrVqiUUCoUA\nxBdffCEUCoXYONReiHmtRUFWuug794Bo+OFWcfrmbSGEEJmFmeLlbS+LoCVB4rOjn4lSfWkVl0Z6\nN+JdEbY8TCTmJv620WAQ4tRKIaZ7CzHNVYjIL4TQ/fazyiksES8tPiZ83vtFjP/hpMjMKxZCCBET\nEyM0Go1QKpUCEMHBwWLz5s1CCCGio6PFvHnzhE6nq9TyPY4eNH8phDCfAYlhYWHyY4WHSAhBREQE\nMTEx2Nvbk5iYyLvvvkujRo1wdXXFwsKCHTt2oIzZbpyEUJDJytbD+SxxF608WjG702ysNdbEpefz\n3rqzHI3NpGNDV758LoQaNnJyyOPsh0s/MP3YdEYFjuLt0LfLDKkxGATTfrnIkkNxaA/N53LkFjQa\nDSqViuLiYjzca3Jjgi0qtQWKV3aDfcVPD6suqmP+qo5lftSWL1/OoUOHSEpKYuPGjTRq1IibN2/S\noUMHJkyYQGfnNL74YCxv9QtDOfxnXlsfy+7oVL55IZTuge5EZ0YzYc8E0gvT+Vfrf9GvXr+qLpIE\nJOUl0XdDX8Lcw/i6y9dlhzHmphifCHhpM3g0gafnQK0QwJiP5+29yuzdMThaa/iwdwB9m9Ri/vyv\n2bRpExEREWg0GiwsLGjTpg316tVj8eLFxMTEULOmXLWqIg+cvx5Fq/2vkr0VD49OpxPr1q0TgLC1\ntTX1Tvj4+Ih9+/aJzMxMUXjjtBCrhgoxxV7ovm4tZu37QAQtCRIT9kwQxbpikV1YIj7fFi0afrhV\nBE3ZJtYcuykMBkNVF016CAwGg/j48MciaEmQWHhmYbn75+2NES5PTxQOXg3E2Suxom/fvsLCwkJo\ntVrRPby16FZHLUa3chK69NjKL4AZqo75qzqW+VFITU0Ver1edO3aVQQGBgp/f3/h7u4uADF58mQx\nYMAAERAQIEq3TBZiir0Qi3uLotxM8fISY+/jssNxQqfXiSXnl4jQ5aGi84+dxdnUs1VdLOkPVlxc\nIYKWBIk10WvKP+D8eiFm1BViioMQG8cLkZtq2nUhIVv0mRMpfN77RfSes1/siU4RBoNBJCUliQED\nBghHR0cBCBcXF1G/fn0RGxsrhBDiyy+/FImJieXfr5p70PwlxzA/Yc6fP8+YMWPw9/cnJycHW1tb\n8vLysLa2RqFQ8EzfvnTw0VBj19toF3eE2P1khL/Lq3UC+C52EwPrD+SjltNZcvAW4TP2MnfvVbr6\nu7Hz7XCea+4lJ/c9IRQKBR+0/IA+dfow59Qcvjr1FQZhKLP/tY71WPKfd/B4cTYv/3iV1//1fwgh\ncHNzIy2niF2xOr47kkn3VoHEnYwgJyengjtKkvRHZ8+e5bXXXsPT05Pdu3cTGRlJdHQ0WVlZZGdn\nM2LECD7++GNGDR3EW60sEYfnQfNXyB70I6/8GMOuS6l8/EwgzRsUMnLbSGZGzaS1R2vW9FlDY9fG\nVV086Q+GNBpCK49WzIyaWWbitUlgPxgfBa1fh9M/wFehEPF/UHibgFr2bHy9LV8+34Tb+aWMWnyc\nHrMi2Rubj0ZjgaenJ9bW1mi1WqytrQkKCmLkyJG8++67LFy48O57SQ9MDsl4ApSUlLB3717c3Nzo\n0KGDqYGcn5+PpaUlO3bsoE19Z06un0ez0uOob18BrQOlTYezzqMOcy4sokhXxCsB75KSEMJPUbfI\nL9HTvr4L/3iqEY09Haq6iNIjojPomHZ4GuuvrqebTzemtpmKvYV9mWMuJeUwZnkUN65dRbn/a5Yt\nnMuJqONMmzaNrCzjusztfTQciTfgUbs2P//8M6GhoVVRnCpVHfNXdSzz35WRkcH27duxsbEhKiqK\nTz/9lFatWnH27Fny8vLw9PRk/PjxLFmyhA0bNtBQcQM2jYeCTOg9k+jaAxi7/AQJtwt5t7czsfp1\n/Br7Kw6WDrzX/D361OkjOzbMWHphOsO2DKNIX8SKnivwsvcq/8C0K8YJ1pe3gIUtNH8ZQkeBkx8l\nOgObzyTybeR1opNzcbO3ZHgrH8I9VRyL3Mtnn33G1atXAbCysqJVq1asWrWK6Ohobt26xbBhw+Rr\nhAfPX7LB/Bg7cuQIH374IXv27OHOj1GtVuPi4kJAo/rkpCXxfIvavNs0D0VGDKAAn7YkNnqKX600\nrIpZR0pBCt5WwejT+xF90xqNSsHTTWrxUls/gmrLhnJ1IIRg2cVlfHHiC5y0TrzX/D26+3ZHqfjt\nA6jsglI+2nSejacTCfCwZ8rTASyd+S+WLVvGj4vn0vu5UaZjHR3seWXMWBITEwkODub111/HxubJ\nX+O1Ouav6ljmv6K4uJiNGzeSmZnJ+PHjcXJyIi0tDYVCgRCCjh07cvjwYZo3b853331HgwYNUGTd\ngB0fGse11gwkt9c8Zp+3ZOnhOBzs8mkbeo79SZtRK9UMDxjOyKCRd/2xK5mn69nXGfHrCFQKFV92\n/JJmbs3ufXDyeTjwBVxYD8IAPu0gZAg06ImwdmJ/TDrf7r/OgavpWKiV+BdHE7N9GWEhjVm5ciVv\nvvkmX331FXq9HmtrawoKCli8eDEvvviiaYk6lUpVSSU3L2bVYN62bRsTJkxAr9czevRoJk+eXOHx\nMvneW0lJCTNnzuTXX3/l4sWLWFhYmBYtt7S0RK1SoRB61ErY905jglVXQRgo0Fhx0yuUS271OGdl\nxemsK8TcNi5fY48/6QktKc5pSICHAwNDPenbpBaudpZVWVSpilzIuMC/D/2bS5mX8LX3Zaj/ULp6\nd8XV2tV0zNZzSfznl4skZhcR6lhIoCqFya+PYuni7/m/jz8kKyubhi5qTibp0RmMqeW1114DoLCw\nkNDQUIYPH46dnd0T18PxJOQvmbMfDp1Ox6JFiygqKmLlypUolUqOHj2KUqnEYDAQGBjIhQsX8PT0\nxNbWlsOHD+Pg4IACIPkcHJmPOPcTQqnmWsMxLNT14dfo2xSQQIMGUSTrD6FAwcAGAxkbPLbM76j0\neLiedZ03975JQm4CzzZ8ljHBY3Cxcrn3CdnxcGaVcahG5nVQKMGzBdTvBr7tiFHXY9mxZH4+GU9+\niZ5gTwf6NrJj0UevEXv9GtnZ2RQVFREcHExWVhaJiYlYW1tTWlrK9u3bqVGjBkqlEiEEDRs2RK1W\nV15lVBGzaTDr9XoaNGjAzp078fT0pHnz5qxatYqAgIB7nlNdk68QgtLSUhITE7lw4QKXLl1Co9Ew\nZ84cUlJSKCkpwd7enoyMDABTr4StVk1hsY53OtsTXFeBk48FiVY2xDu6ccPKmpuihNSSbNN9LJQ2\nWOi8uZ3uR3FOAG5WnjzdxIMBzTzx95A9E5JxiMaOuB0svbiUixkXAWjk1IhA50ACXQKp51gPF0sP\nNp7I5fuDcWTml1DHxYa+IbWwSL1IbcVtrC6t5b1vtxOdpkepVGBpacntvCLTPTp16sTx48extLTE\nzc2NsWPHolAoCAsLw9nZGQsLC3x8fB67BvXjnr9kzn4wOp2OkpISDh48SExMDJs3b6aoqIijR4/i\n4OBAcnIyarUanU6H1sqK4qJiPPwakHorload+tOo18uUqrSoi2/ToPQy/rqLtNcdxY94CrFkraEj\n80r6kKy0ws4pGie3c2QaLmGltmJA/QGMCBhBLdtaVV0N0t+QU5LD7BOzWRezDoBWHq1o4dGChjUa\nUtO6Jq5WrlioLNAoNaiVamNOFAIST8GVbXB5q/EPLAC1FtyDKXFpxOkiDzbcsOR0lpbUEkt8a1gR\nVs8DUq8we/q/SUlJMeVXtVqNpaUlubm5WFpaUlxczLPPPsv58+dp2rQper2eL774gtjYWOzt7XF2\ndsbDw+Oxy8/lMZsG8+HDh5k6dSrbt28HYPr06QC8//779zznryTf1NRU8vLyqFOnDpmZmVy4cIGa\nNWvSsGFDkpOTOX36NH5+fjRs2JCbN28SFRVFQEAAjRo14urVqxw/fpzAwEC0Wi2ZmZlERERQp04d\n7OzssLGxISIiAi8vL2xsbHB3d2fXrl24urqi1+spKiri1q1b2NjYYDAYUCqVJCYmYjAYTIkyJSUF\nfUkRSvSkpmWAEKTfzsLW2oqk1HSUCgX5hUXYWGvJy//t2fJKpQLD/3rolErjg4DcXFQU6wwEhtlS\nYq3BpXtNktQqdNqyL1xrlQN2KndU+poUFTqRcdue/LyaiBJn/Fzs6B7oRs8gD4JrO5ieBiVJvyeE\n4FrWNXbf3M2JlBNcyLhQ5kEnlipLPGxqodI7k55tQVq2GqGzQYUtte2d8LNR0Kz4DJ4ZZ7hxPpod\nZwo4EqvD0kKFnZWWSwn5pmvVdLIjNTMXAKVCgUdNZxJS0lEqlTja21LH25OrcbdAAQ3q+lGnQQBn\nzpwx9dTVrl2b8+fPU6NGDRo2bIi9vT3nz5/HwcEBf39/3N3dSUlJwcLCgpo1a+Lo6EhycjLu7u6E\nhISQkpJCQkICoaGh2Nv/9T8cH/fGY2Xl7NzcXJKSkvD19cXCwsLU21W/fn00Gg0ZGRkkJibSqFEj\nNBoNV69e5ezZs/To0YP8/HzWrl2LwWCgX79+XLt2jW3btqHT6XjjjTc4f/4869evR6fTMWLECOLi\n4ti8eTMKhYJRo0Zx/fp1Nm7ciI2NDT169CA2Npbdu3fj6OhI27ZtSUhIYOfOndjZ2REQEEBWVhZH\njx7FysoaoVCgUWtISoxHpVKj05WiVmvQ6UpNZVOqVBj0etRqDTb2DjjV9iE7LQnvuvUJbxuGs7oQ\nd00hnpocPEhGKFOwErcpVigoVKi4qfXjsl0gV6xrk6vMJkdcI734BgKBj70Pfev25dkGz1JDW+Mv\n/IQlc3Uj5wYbrm5g542d3Mi5cc/j1Eo1WpUWOws705e9SkuN0mIc87OokZeGQ04yNYrysDMY0CBQ\nCYFagE5owGCJpU5LcpEllzMhpUDJ8sgbXE/ORmBsiwuMS9n9vml455ORO69vGzs7CvMLsHOsQWlJ\nCY5Ozuh0pXj6+FGQnY2HpydqtQqXmm5kpKXi6eWNhUqBu6szaWlp1K1bF41Gg62tLTk5OdSuXRtL\nS0sKCwsxGAymRQtu376NhYUFXl5eqFQqDAYDxcXFODs7U1paikqlQq1W4+HhgVL54GtYPGj+emR9\n7gkJCXh5/TaY3dPTk6NHjz70+3z00UesX7+elJQUFi5cyPvvv4+npye3bt3im2++YerUqdSpU4dr\n167xzTffMH36dPz9/blw4QILFixg1qxZNGrUiAsXLtC+fXsiIyOxsLCgpKTE9EQ8jUZDaWkprVq1\n4siRI6bv/44U4E5TVa2GvPxClDZKMIDGSQNKcO7ljD5Tj4WbBWpbNVZ1rLCwVKPR2FHL2o2zNy0Q\n+Y4YsmogSh0xlNbAUFqDXIMVKUBNO0vqutrSoYEtYb41aO7rRC1Hq79b5VI1oFAoqFejHvVq1AOM\nDej4vHjisuNIyEsgPjeehLwEEvIS0NrfwtbiNiWGEsD42k4xwBEN4A64e0NXcPvftXsnKJl2JY3I\ny7fp5A0WqlJe3QLxueBtDwPrZPPfFDAYDOTl5GCbfZmsHD0Ax0+eJT0rj+vXrwNw5coVateuTXx8\nPGAci3dnfCgYE72rqyspKSmm/c7OzqSmpgLw008/MW3aNM6dO8eqVasYPHjwo69cM1VZOXvTpk28\n8MILXLlyhfr16/Pzzz/z8ssvExcXh4+PDz/99BOvvvoqSUlJuLu7M2XKFH744QdOnDjB9u3b+eCD\nDwCIiYlh9uzZpuuWlJSU+X7x4sWmT+MA1q1bh0qlQq/Xm+L4vT179pQ5/uLFi6aGQm5uHigUgLGH\nT6dQorJ3RSjVKIoL6e1dwHP+SkLcwc5Si6e9ErWyBLjz9LZT//vC+FG6hQvJTt50U2uB369jngcc\nhRKwt7An0DmQ59x606ZWGxq7NH4ievWku/nY+zCh2QQmNJtAZlEmsdmxpBWkkVGUQYm+BJ1BR6mh\nFJ1BR6GukNySXHJLcskpySG+MJULRdncLr5NqbIUHK2A8t/nmwoH3s91o0ZhDu0d87DU5/OcjwNJ\nGcGPeQ4AACAASURBVEpaupeSXyz44VwpF9J0WKgUZBUaSC2AS2kGsopAZ9CjVEFRQS4GA2RnpgMK\nCvKMnSmpicY8HH3x7APXwZ3ebYCOHTty+vTp3yaVt29PWloaGo2G3NxcmjRpQmxsLJaWlri4uPDT\nTz9VyjyZR9ZgLq/jurxf9oULF5qWPLnzJvcgXnrpJbp16wbA008/TWlpKY0bG5fTef7557G2tiYw\nMBCAkSNH4ubmZvr+1VdfpX79+vj5+ZGeno6Liwtr167F3t4ee3t72rZty4YNG3B0dMTJyYnGjRuz\ndetWXF1dKS0tJSoqCldXV9RqNVZWVqSlpeHm5oatrS22trakpaXh7e2NkzIHV1UhFpaW5BeVUs/X\nEyenGlhbWZNXVEoWRVwxpGBpZYfKwg6N1g61hR3q/30Mo1VrcbR0xNHSESu1lSmpbz6bhIVKgYVa\niYVKhYVaibWFCmdbC2pYW6DVVM+B/NLDp1Ao8LLzwsuu/BndQggKdYXcLr5NTnEOxfpi8kuKuF1Y\nQFZhAXklJRSW6tAbDLgF+WHb14fuBoEoyaWlp5Ybc0qgJM/4pS9lekkxGZm3sbHUYGttwcWYOHYe\nOk2bJg3xf/o1Vq1axYEDB+jatStt2rRh+fLlxMfH06xZM5o2bcqyZctITk4mNDSURo0akZycTHx8\nPEIIvL29SU9Pp3bt2rRu3ZqpU6dy+vRpWrduXcm1al4qK2e3adOGFStW4OZm/BOqU6dOrF69GhcX\n4/jN7t27s3btWhwdjY9wfuWVV3B3d8fHx4fevXtz7NgxatasyeDBg3F3d2f37t3Y2toyfPhwvL29\niYyMxN7eHn9/f4qKioiNjcXZ2RkfHx9KS0u5efMmTk5OZGdno1AocHZ2xs3NjaSkJDQaDU2aNMHZ\n2ZmbN2+i1WoJDAwkT6fkUkYpNtbWaFRKNColapUCtVKJRqWgVuJ2bDQKrK2s0Kg1oNKAUv2/f//3\nvVUN45elPSiVOOqK+OzmbrQqLRYqC7Rq47/Wams8bDywtbB94LqVHn9OWiectE4PfJ4QggJdAVnF\nWWQVZZFTkoPOoENn0KEXenQGHU5aJ/w9Wtx1bj0AgwGL0nxeL8qB0gLQFUFpkfHfO18GPQgDBoOB\nopJiMpybY7CrxdXrsURHX6ZYJ9Da2nP1ygWiIvfhXa8hVjZ2pCXHkxhzkZZhIVhaWpKTk0NWVhZB\nQUE4OzuTmJiIpaUlOp0OKysrmjVrRlxcHNeuXUOr1dKqVSs0Go2p17lRo0bk5xs/pbSwsMDSsnLm\nXT32QzIkSZLMweOev2TOliSpOnnQ/PXIHlzSvHlzYmJiiI2NpaSkhNWrV9O3b99HdTtJkiTpb5A5\nW5Ik6d4e2ZAMtVrN3Llzeeqpp9Dr9bz00kumoRCSJEmSeZE5W5Ik6d4e6UJ7vXr1olevXo/yFpIk\nSdJDInO2JElS+R7ZkAxJkiRJkiRJehLIBrMkSZIkSZIkVUA2mCVJkiRJkiSpArLBLEmSJEmSJEkV\neGTrMP8VLi4u2NjY4OrqWtWhVCgtLc2sY5Tx/X3mHqOM7+972DHGxcWRnp7+0K73OHBxccHX17eq\nw3hkHofX8aMm68BI1oPRk1QPD5qzzarBDI/HQvjmHqOM7+8z9xhlfH/f4xCjVLXka0TWwR2yHoyq\ncz3IIRmSJEmSJEmSVAHZYJYkSZIkSZKkCqimTp06taqD+KPQ0NCqDuG+zD1GGd/fZ+4xyvj+vsch\nRqlqydeIrIM7ZD0YVdd6MLsxzJIkSZIkSZJkTuSQDEmSJEmSJEmqgNk0mCdNmkT79u0ZNmwYJSUl\nd+1fvXo1nTt3pkOHDhw7dqwKIqw4xoiICLy8vOjYsSNdunQxu/jumD59OmFhYZUcmVFF8e3cuZN2\n7drRrl07hg8fjl6vN6v4tm7dSps2bWjXrh3jx4+v9NjuqCjGa9eu0bRpU7RaLXl5eVUek06nY9So\nUbRv354JEyZUWjzluVeMVVVnkvm5X/6sytxZWSqqA3N4D64s96qHwsJC+vTpQ3h4OF27diUzM7MK\no3y0cnNzadmyJba2tpw/f77MPnPK7ZXJLBrMp06dIikpicjISAICAli7dm2Z/YmJiWzcuJHdu3ez\nf/9+WrRoYXYxAjz//PNERESwe/dus4wvNzf3rhd+ZblffOHh4Rw4cIADBw6gVqs5dOiQWcUXFBTE\n/v37OXDgAJmZmRw/frxS4/szMXp4eBAREUGrVq3MIqbNmzdTu3ZtIiMjKSgoqPSf6Z+JsSrqTDI/\n9/vdqsrcWVkqqgNzeA+uLBXVw6+//kpQUBD79u3j+eefZ/ny5VUY6aNlZWXFL7/8wqBBg+7aZy65\nvbKZRYP58OHDdO/eHYAePXrcVfnbtm3D0tKSbt26MXz48CrpCbpfjADr1q2jffv2zJ49u7LD+1Px\nzZ49m9dff72yQwPuH5+FhQUAQgiEEPj5+ZlVfN7e3qjVagA0Go3p/+YUo7W1NQ4ODmYT0595TVZ1\njFVRZ5L5ud9rtSpzZ2WpqA7M4T24slRUD/Xr16egoACArKysJ+YBHuVRq9X3LJ+55PbKZhYN5qys\nLOzt7QFwcHC462OOlJQUsrKy2LlzJ23atGHu3LlmF2NYWBiXL19m9+7dbNu2jRMnTphVfNnZ2Zw7\nd442bdpUalx33C8+gOXLlxMYGFglTxL6M/EBnDhxgvT0dJo2bVqZ4QF/PsbKVFFM5hKvucQhma+K\nXiNVnTsrS0V1YA7vwZWlonqoW7cu58+fJygoiGXLltGvX7+qCrNKVdecWqndZMnJyeV27/fs2ZOc\nnBzA+INwcnIqs9/R0ZFOnTqhUCjo3Lkzn3zyidnFaGtra/p/3759OXPmzCNZeuWvxjdr1qxKGXv7\nV+MDGD58OMOHD+f1119n/fr1DB482Kzii4+PZ8KECaxfv/6hx/WwYqxsNWrUuGdMFe0zlxglCSp+\njVRW7qxqFdVBZb4HV7WK6mHp0qV07NiRjz76iJ9//plp06bx2WefVVWoVaa65tRK7WF2d3c3jVP9\n/VevXr3YsWMHANu3b6dt27Zlzmvbti2nT58GjOOL6tSpY3Yx3nnxAERGRlKvXj2ziu/q1at88skn\n9OjRg5iYmEf2S/5X4ysuLjb9397eHhsbG7OKLy8vj6FDh7JgwYJH3vv9V2OsCq1atbpnTBXtM5cY\nJQkqfo1UVu6sahXVQWW+B1e1++WLO41DR0dHsrKyKj0+c1Btc6owExMnThTt2rUTQ4cOFcXFxUII\nIcaMGWPa//7774vw8HDRo0cPkZGRYXYxfvvtt6J58+aidevWYuLEiWYX3++FhoZWdmhCiIrjW7hw\noQgPDxcdOnQQY8aMEXq93qzi+/TTT0WtWrVEeHi4CA8PFxEREZUe3/1izMzMFF26dBGOjo6iY8eO\nYvv27VUS0514SktLxYsvvijatWsn3njjjUqJ5UFjrKo6k8zPvV4jv1dVubOyVFQH5vAeXFnuVQ/Z\n2dmiV69eIjw8XLRt21Zcvny5iiN9tHr27Ck8PDxEq1atxNKlS80yt1cm+eASSZIkSZIkSaqAWUz6\nkyRJkiRJkiRzJRvMkiRJkiRJklQB2WCWJEmSJEmSpArIBrMkSZIkSZIkVUA2mCVJkiRJkiSpArLB\nLEmSJEmSJEkVkA1mSZIkSZIkSaqAbDBLkiRJkiRJUgVkg1mSJEmSJEmSKiAbzJIkSZIkSZJUAdlg\nroaSk5MZPHgwdevWJSAggF69enHlypWHeo+IiAgOHTr0UK5VXFxM165dCQkJYc2aNURGRhIYGEhI\nSAiFhYUPdK0NGzZw8eLFe+6fNWsWy5YtA2DkyJGsXbu2zH5bW9sHL8Aj0KtXL7Kysio8ZuLEiezZ\ns6eSIpIkqTKpVCpCQkJMX3FxcURERNCnT59Hcr+OHTsSFRX1SK79MCxZsoTExMRKudeCBQtM7xMV\nxTN+/Phy93366aePIizpEZMN5mpGCEH//v3p2LEj165d4+LFi3z66aekpKQ81Ps8zAbzqVOnKC0t\n5fTp0zz//POsXLmSiRMncvr0aaysrB7oWhU1mHU6Hd9//z1Dhw59GGE/Ulu3bsXR0bHCY9544w0+\n++yzSopIkqTKZGVlxenTp01fvr6+D+3aOp3uoV2rslRmg3ncuHGMGDHiL58vG8yPJ9lgrmb27t2L\nRqNh3Lhxpm0hISG0b98eIQSTJk0iKCiIxo0bs2bNGoC7ei3Gjx/PkiVLAPD19WXKlCk0a9aMxo0b\nEx0dTVxcHAsWLODLL78kJCSEyMhI/Pz8KC0tBSAnJwdfX1/T93ekpaUxcOBAmjdvTvPmzTl48CCp\nqam88MILnD59mpCQEL755ht+/PFHpk2bxrBhwwD4/PPPad68OcHBwUyZMsV0vWXLlhEcHEyTJk0Y\nPnw4hw4dYtOmTUyaNImQkBCuXbtW5v579uyhWbNmqNXqP1WX5d03Li4Of39/XnnlFQIDA+nevbup\nF7xjx4689957tGjRggYNGhAZGQmAXq9n0qRJpmt98803pnrv0KED/fv3JyAggHHjxmEwGEz1np6e\nXuH9fHx8yMjIIDk5+U+VR5KkJ0dmZib9+vUjODiYVq1acfbs2Qq3T506lTFjxtC9e/d7NgZXrFhB\nmzZtCAoK4tixYxgMBurXr09aWhoABoOBevXqkZ6efte527Zto1mzZjRp0oQuXbrcN5aZM2eazg0K\nCiIuLu6e+W7t2rVERUUxbNgwQkJC2LJlC/379zedv3PnTgYMGFAmnmPHjpm2bdy4ESsrK0pKSigq\nKqJOnToAXLt2jR49ehAaGkr79u2Jjo6+K77jx48THBxM69atTe+fdyQmJtKjRw/q16/PP/7xDwAm\nT55MYWEhISEhpvcw6TEhpGpl9uzZ4q233ip339q1a0XXrl2FTqcTycnJwsvLSyQmJoq9e/eK3r17\nm457/fXXxeLFi4UQQvj4+Ig5c+YIIYSYN2+eePnll4UQQkyZMkV8/vnnpnNGjhwp1q9fL4QQ4ptv\nvhHvvPPOXfcfMmSIiIyMFEIIcePGDdGoUSMhhLjr/i+++KL46aefhBBCbN++XbzyyivCYDAIvV4v\nevfuLfbt2yfOnz8vGjRoINLS0oQQQmRkZNx17h999NFHprLcOdbX11c0adLE9GVjY1PhfWNjY4VK\npRKnTp0SQgjx7LPPiuXLlwshhAgPDzeVe8uWLaJLly6m+vj444+FEEIUFRWJ0NBQcf36dbF3715h\naWkprl27JnQ6nejataspdh8fH5GWllbh/YQQYvTo0WLt2rXllleSpMeXUqk05aV+/foJIcrmyvHj\nx4upU6cKIYTYvXu3aNKkSYXbp0yZIpo1ayYKCgrKvV94eLgYPXq0EEKIffv2icDAQCGEEFOnThVf\nfvmlEMKYFwcMGHDXuampqcLT01Ncv35dCPFbPq4olt+/fwQGBorY2Nj75tfjx48LIYQwGAyiYcOG\nIjU1VQhhfG/ZtGlTmZhKS0uFr6+vEEKId999V4SFhYkDBw6IiIgIMXjwYCGEEJ07dxZXrlwRQghx\n5MgR0alTp7viCwwMFAcPHhRCCPHee++Z6mXx4sXCz89PZGVlicLCQuHt7S1u3rwphBCm9xHp8fLn\nutKkauHAgQMMGTIElUqFm5sb4eHhHD9+HHt7+wrPu/NXemhoKD///HO5x4wePZoZM2bQr18/Fi9e\nzLfffnvXMbt27SozXCInJ4fc3NwK771jxw527NhB06ZNAcjLyyMmJoYzZ84waNAgXFxcAHBycqrw\nOgBJSUn4+/uX2fb5558zaNAg0/d3xjDf677e3t74+fkREhICGOskLi7OdP7v6+rO9h07dnD27FnT\neOns7GxiYmKwsLCgRYsWpt6OIUOGcODAgTLxABXer2bNmpX2MaUkSZXnzpCMezlw4ADr1q0DoHPn\nzmRkZJCdnX3P7QB9+/atcJjbkCFDAOjQoQM5OTlkZWXx0ksv8cwzz/DWW2/x/fffM2rUqLvOO3Lk\nCB06dMDPzw/4LR9XFMu9VJTv7lAoFAwfPpwVK1YwatQoDh8+fNeYY7VaTb169bh06RLHjh3jnXfe\nYf/+/ej1etq3b09eXh6HDh3i2WefNZ1TXFxc5hpZWVnk5ubSpk0bAIYOHcovv/xi2t+lSxccHBwA\nCAgI4MaNG3h5eVVYPsl8yQZzNRMYGHjXRLY7hBDlbler1aahAABFRUVl9ltaWgLGSSj3GvvWtm1b\n4uLi2LdvH3q9vszHVncYDAYOHz78QOOShRC8//77jB07tsz2OXPmoFAo/vR1wPgG9MeyPeh94+Li\nTPUBxjr5/cTE8upKCMFXX33FU089VeZaERERd5WhvDJVdL+ioqIHHuctSdLjr7x8rlAo7rkdwMbG\nxrRt1KhRnDp1ilq1arF169Yyx/3+PC8vL9zc3NizZw9Hjx5l5cqV6PV6QkNDAWMjPCwsrNzcda9Y\nKnrPqSjf/d6oUaN4+umn0Wq1PPvss+UOtWvfvj2//vorGo2Grl27MnLkSPR6PTNnzsRgMODo6Fjh\nHyX3es+8V6yP49hw6TdyDHM107lzZ4qLi8v08B4/fpx9+/bRoUMH1qxZg16vJy0tjf3799OiRQt8\nfHy4ePEixcXFZGdns3v37vvex87O7q7e4REjRjBkyJByeyAAunfvzty5c03fV5So7njqqaf4/vvv\nycvLAyAhIYHU1FS6dOnCjz/+SEZGBmAcK3evuO7w9/fn6tWr971nRff9K5566inmz59vGtN95coV\n8vPzAeM4u9jYWAwGA2vWrKFdu3YPdO0rV66U+8eJJElPtg4dOrBy5UrA+Me3i4sL9vb299z+R4sX\nL+b06dOmxjJgmtdy4MABHBwcTL2no0eP5oUXXuC5555DpVKhUqlMkxGnTZtG69at2bdvH7GxscBv\n+fhesfj6+nLy5EkATp48aTqvIn/M7bVq1aJWrVr85z//YeTIkfeso1mzZtG6dWtcXV3JyMggOjqa\nwMBA7O3t8fPz46effgKMjeMzZ86UOb9GjRrY2dlx5MgRAFavXn3fOAE0Gs1dc3gk8ycbzNWMQqFg\n/fr17Ny5k7p16xIYGMjUqVOpVasW/fv3N02S69y5MzNmzMDd3R0vLy+ee+45goODGTZsmGkYQkWe\nfvpp1q9fb5r0BzBs2DBu375t+ljvj+bMmUNUVBTBwcEEBASwYMGC+96ne/fuDB06lNatW9O4cWMG\nDRpEbm4ugYGB/POf/yQ8PJwmTZrwzjvvADB48GA+//xzmjZtetekv549e7J///773rOi+/4Vo0eP\nJiAggGbNmhEUFMTYsWNNPRGtW7dm8uTJBAUF4efnV2Yiy/2UlpZy9epVwsLC/lJckiQ9vqZOnWrK\np5MnT2bp0qUVbv8zatSoQZs2bRg3bhyLFi0ybe/bty95eXn37AxxdXVl4cKFDBgwgCZNmvD8889X\nGMvAgQPJzMwkJCSE+fPn06BBg/vGNnLkSMaNG1dmudFhw4bh5eVFQEBAuee0bNmSlJQUOnToAEBw\ncDDBwcGm3vCVK1eyaNEimjRpQmBgIBs3brzrGosWLWLMmDG0bt0aIYTpj4iKjBkzxvR+Kj0+FOJ+\nnylI0kOydu1aNm7cyPLly6s6lHvq378/M2bMoH79+lUdChEREcycObPMmLgHsX79ek6ePMnHH3/8\nkCOTJEn6TVRUFG+//bapc8RcjB8/nqZNm/Lyyy8/snvk5eWZ5rZ89tlnJCUlMXv27Ed2P6nqyDHM\nUqV44403+PXXX8t8vGeO7iQ8c2gw/106nY533323qsOQJOkJ9tlnnzF//nzT0ApzERoaio2NDf/9\n738f6X22bNnC9OnT0el0+Pj4mJZclZ48sodZkiRJkiRJkiogxzBLkiRJkiRJUgVkg1mSJEmSJEmS\nKiAbzJIkSZIkSZJUAbOa9Ofi4oKvr29VhyFJkvTA4uLiSE9Pr+owKpXM2ZIkPa4eNGebVYPZ19eX\nqKioqg5DkiTpgZn7etd6vZ6wsDBq165911KFQggmTJjA1q1bsba2ZsmSJTRr1uy+15Q5W5Kkx9WD\n5mw5JEOSJKkamD17Nv7+/uXu+/XXX4mJiSEmJoaFCxfy6quvVnJ0kiRJ5k02mCVJkp5w8fHxbNmy\nhdGjR5e7f+PGjYwYMQKFQkGrVq3IysoiKSmpkqOUJEkyX7LBLEmS9IR76623mDFjBkpl+Sk/ISEB\nLy8v0/eenp4kJCRUVniSJElmz6zGMEuSOSktLSU+Pp6ioqKqDkUyI1qtFk9PTzQaTVWH8qf88ssv\n1KxZk9DQUCIiIso9prznVykUinKPXbhwIQsXLgQgLS3tocUpSX+XzNlSeR5Wzn6kDeYvv/yS7777\nDoVCQePGjVm8eDFarfZR3lKSHpr4+Hjs7Ozw9fW9Z+NBql6EEGRkZBAfH4+fn19Vh/OnHDx4kE2b\nNrF161aKiorIycnhhRdeYMWKFaZjPD09uXXrlun7+Ph4atWqVe71xowZw5gxYwDzn+goVS8yZ0t/\n9DBz9iMbkpGQkMCcOXOIiori/Pnz6PV6Vq9e/ahuJ0kPXVFREc7OzjLxSiYKhQJnZ+fHqgdr+vTp\nxMfHExcXx+rVq+ncuXOZxjJA3759WbZsGUIIjhw5goODAx4eHlUUsST9NTJnS3/0MHP2I+1h1ul0\nFBYWotFoKCgouGePhSRVhsSsQtaeiCfhdiFNvBwZGFobS7WqwnNk4pX+6El5TSxYsACAcePG0atX\nL7Zu3Uq9evWwtrZm8eLFVRydJJXvcuZldtzYgRCC/vX642XvVWb/k/L7KT08D+s18ch6mGvXrs3E\niRPx9vbGw8MDBwcHunfv/qhuJ0n3pNMbmB9xjY4zI/hy1xV2XUrhg/XnGP7dMfKKdVUdXoUUCgXD\nhw83fa/T6XB1daVPnz73PdfW1hYwLs7+ww8/mLZHRUXx5ptvPpT4/sy1Tp8+zdatWx/ounFxcSgU\nCr766ivTtvHjx7NkyZK/EuZf1rFjxydqneGOHTua1mAeN24c48aNA4yvs3nz5nHt2jXOnTsnh1pI\nZmnztc0M3jKYRecW8f3573lm4zMcSTpS1WGVIXP2k5uzH1mD+fbt22zcuJHY2FgSExPJz8+/62NA\nME4gCQsLIywsTE4gkR66M7eyGLjgMP+3LZrODWty4L3ORH3YlVnPhxB1I5OPNp6v6hArZGNjw/nz\n5yksLARg586d1K5d+4Gu8cfkGxYWxpw5c/52bDqd7k9d668kX4CaNWsye/ZsSkpK/nJ8kiQ9GY4n\nH+fDgx/SrGYz9j63l+0Dt+Nj78Obe97kRs6Nqg7PRObsJzdnP7IG865du/Dz88PV1RWNRsOAAQM4\ndOjQXceNGTOGqKgooqKicHV1fVThSE84g0FwNTWPvZdT2XAqgW/2XWP4oqM8M+8g8ZkFfDWkKfNf\naEZtRysUCgX9mtbm9U71+PlkAkevZ1R1+BXq2bMnW7ZsAWDVqlUMGTLEtG/q1KnMnDnT9H1QUBBx\ncXFlzp88eTKRkZGEhITw5ZdfEhERQZ8+fTAYDPj6+pKVlWU6tl69eqSkpLB582ZatmxJ06ZN6dq1\nKykpKab7jRkzhu7duzPi/9m787goq/2B459ZgBl2UUAFlcUNEATXUjE0LXclFyzvdctss59W1xYr\nMzNTK628lVrdUjOxNPct98zcUEERRVBRUGQHWWaGWZ7fH5OjBKYmw+Z5v1739YrnOc9zvg93OJ45\nzznfM3q05V4AR44coUuXLoSFhdGlSxcSExMpLS1l+vTprFq1itDQUFatWkVxcTHjx4+nY8eOhIWF\nsX79+gqf293dnUcffZSlS5eWOxcbG8tDDz1ESEgIkZGR5OXlAebRhWnTpvHII4/w2WefMXbsWJ5/\n/nl69OiBn58f+/btY/z48QQEBDB27FjL/Z5//nk6dOhAUFAQ77777j38vyMIgrUVlRbx5v43aeLU\nhM97fk49VT08HTz5qtdXyGVyPo75+M43qUKiza6bbbbVOsxNmzbl0KFDlJSUIEkSu3btuu0uU4Jw\nP46m5NJr/j56zd/HuO+OMmVVLB9uPcuVPA1TerVg32s9GNi2cbl5TC9ENMfT2Y6Pf02spsjvzsiR\nI4mOjkar1XLy5Ek6d+58T9fPmTOH8PBwYmNjefnlly3H5XI5gwcPZu3atQAcPnwYHx8fPD096dat\nG4cOHeLEiROMHDmSefPmWa47duwY69evLzMCAtC6dWt+++03Tpw4wcyZM5k2bRq2trbMnDmTqKgo\nYmNjiYqK4oMPPqBnz54cPXqUPXv2MHXqVIqLiyuM/Y033uCTTz7BaDSWOT569Gjmzp3LyZMnCQ4O\n5r333rOcy8/PZ9++fbz66quA+W3X7t27WbBgAQMHDuTll1/m9OnTnDp1itjYWAA++OADYmJiOHny\nJPv27ePkyZP39DsWBMF6/hf/PzJKMpjdbTYONg6W4w0dGvJM8DPsTd3L0WtHqzHCskSbXTfbbKst\n+uvcuTPDhg2jXbt2KJVKwsLCLKmIBKGyHLuUy6ivD9PIVcWcJ4Jp7uFIPQdb6tnb4uZg+7fXqm0V\nPBPux6zNZ4i/UkAbL5fbln1v42kSrl6v1NgDGzvz7sCgO5YLCQkhJSWFlStX0q9fv0qNISoqipkz\nZzJu3Diio6OJiooCzOmZoqKiSE9Pp7S0tEw6nkGDBqFWq8vdq6CggDFjxpCUlIRMJkOv11dY56+/\n/sqGDRssoyxarZbLly9X+IXa19eXTp06lWnoCwoKyM/P55FHHgFgzJgxDB8+vMwz3WrgwIGW1Jae\nnp4EBwcDEBQUREpKCqGhofz0008sWbIEg8FAeno6CQkJhISE3NXvUBAE68ksyWR5wnL6+vYlxL38\n3+S/Av/FsoRlLEtYxguNXrAcF222aLMrm1V3+nvvvfc4e/Ys8fHxLF++HDs7O2tWJzxgNKVGKLEK\nvAAAIABJREFU/m9lLI1cVax7oSsjOzWlg48b/u6Od+ws3zC8QxPUNgpWHK45c+AqMmjQIP7zn/+U\nebUHoFQqMZlMlp/vNXXOww8/THJyMllZWaxbt44nnngCgJdeeolJkyZx6tQpFi9eXOa+Dg4OFd7r\nnXfeoUePHsTHx7Nx48bbxiJJEmvWrCE2NpbY2NjbNrw3TJs2jblz55Z5zr/z1/hutDtyubxMGySX\nyzEYDFy8eJGPP/6YXbt2cfLkSfr371+r0sYJQl227PQy9CY9L4W9VOF5O4UdQ1sM5be03zCajBWW\nqQ6iza57bbbY6U+otb79/QJX8jWsmvgQ9e6yg/xXLmob+rRpyOaT6cwYFHTbNHN3M6pgTePHj8fF\nxYXg4OAyu7X5+PhYsh4cP36cixcvlrvWycmJwsLCCu8rk8mIjIzklVdeISAggPr16wPmEYEbC1Uq\nmo9WkVuvuXVl9F/rf/zxx1m4cCELFy5EJpNx4sQJwsLCbnvf1q1bExgYyKZNm+jUqRMuLi7Uq1eP\n/fv3Ex4ezvLlyy0jF//E9evXcXBwwMXFhYyMDLZu3UpERMQ/vp8gCJWjsLSQ1UmreazZYzRxanLb\ncsNbDufb+G8pNtycJiDa7DsTbfa9seoIsyBYi1Zv5Ps/Uoho5U5nv/r3da9BoY25rjXw27nsSoqu\n8nl7ezN58uRyx4cOHUpubi6hoaF89dVXtGzZslyZkJAQlEolbdu2ZcGCBeXOR0VF8cMPP5R5LTZj\nxgyGDx9OeHg4DRo0uKsYX3vtNd588026du1aZv5ajx49SEhIsCwgeeedd9Dr9YSEhNCmTRveeeed\nO977rbfeIi0tzfLz0qVLmTp1KiEhIcTGxjJ9+vS7irEibdu2JSwsjKCgIMaPH0/Xrl3/8b0EQag8\nvyT9QrG+mLFtxv5tuUaOjejYsCNag7bCbd6rg2iz616bLZNqyqcLc+qUupTzVLCe9bFXmBwdy/Kn\nOxHe4v6yq5QaTLR7fwcD2zbmwyeCLcfPnDkjFqoKFaros/Egtl8P4jMLVcMkmRi4diAN1A1Y2vfO\nI6Y/Jf5E/ev16RrWFZVSVQURCrVJZbTZYoRZqJXWx16lsYuKrv53903679gq5XRr3oC9iZk1ZnRC\nEAThQXYo/RCXCy8zvNXwOxcGHm36KAAFugJrhiU8wESHWah1Ckr0/HYui4FtGyOXV86Wlz1au5Ne\noCUxo+J5Y4IgCELVWX1uNa52rvRu1vuuytdX18dOYUehXrThgnWIDrNQ6/xxPhuDSaJXoGel3TOi\nlQcAe86K3SYFQRCqU4GugL2pe+nv1x87xS3ZtXSFEPsjHPgcrsaWu85OYYfOoENvrDg9miDcD5El\nQ6h1fk/OxtFOSWgT10q7p6ezisBGzuxJzOT5CP9Ku68gCIJwb7anbEdv0jPQf+DNgxd/g9XjofiW\nQY2OE6DPXFCYuzJ2SnPnukhfRD1FvaoMWXgAiBFmodb5PTmbh/zcsFFU7sc3vGUDTlzOQ6uvObk8\nBUEQHjQbz2/E38WfQLdA84HkXfDDUFC7wfjtMPU8PPQiHP0GdtzM2GAjt0EpV1KkL6qmyIW6THSY\nhVolNbeESzkldG1+/4v9/qqTjxt6o8SJy/mVfm9BEAThzi5fv0xsViwD/c27vZFzHn4aAw1awdPb\noelD4NAA+syGzs/BoS8hcZvlekcbR4r1xWIBt1DpRIdZqFX2J5lzJYe3qPwOc4dmbshkcDQlt9Lv\n/U85OjqW+XnBggWoVCoKCm6uBN+7dy8uLi6EhoYSGhpKr169qjpMoYbTarV06tSJtm3bEhQUxLvv\nvluuzF8/RzNnzqyGSIUH3cYLG5Eho79ffzDoYPU4kCvgyZWg/ss0i97vmzvSW18DvQYABxsHjCYj\nOqOuGqIXbXZdJuYwC7XKoQs5eDrb4e/ueOfC98jF3oZWnk41qsP8VytXrqRjx46sXbuWsWPHWo6H\nh4dbdo8ShL+ys7Nj9+7dODo6otfr6datG3379uWhhx4qU058joTqZJJMbDy/kc6NOtPQoSFseQ3S\n42DkSnCtYKc/pS30mwfLBsOx78ElAnsbewCK9cU1Ih+zaLPrDjHCLNQqcWn5hDWpZ35VZwUdfdw4\nfikPg9Fklfvfj/Pnz1NUVMSsWbNYuXJldYcj1CIymcwy8qXX69Hr9Vb7GxKEf+pE5gmuFF1hkP8g\nSNgARxab5yq37nf7i/wioFk3+P1TkCRsFbbYyG0oMZRUVdi3JdrsukV0mIVaI7+klEs5JYQ0cbFa\nHR193SguNZKQft1qdfxTK1eu5MknnyQ8PJzExEQyMzMt5/bv3295vffBBx9UY5RCTWU0GgkNDcXD\nw4PevXvTuXPncmUOHjxI27Zt6du3L6dPn66GKIUH2YbzG1Ar1Txq3wzWvQBe7aHXjDtf2P1VKLoG\nenMn2cHGoUbMYxZtdt0ipmQItUZcmnkOWKh35aWT+6tOPm4AHE3Jo0v9W05sfQOunarcyhoGQ985\nd108OjqatWvXIpfLeeKJJ/j555958cUXAfF6T7gzhUJBbGws+fn5REZGEh8fT5s2bSzn27Vrx6VL\nl3B0dGTLli0MGTKEpKSkcvdZsmQJS5YsASArS+QtFyqH1qBle8p2entHYL96PCjtYMQy87SLO/Hr\nAW5+UGrOjmFvY49q5wykvDRkskocFxRt9gPNaiPMiYmJlm9PoaGhODs78+mnn1qrOuEBcDLVnL2i\njbf1Rpgbuqho6KziZFrNypRx8uRJkpKS6N27Nz4+PkRHR4tXfMI/4urqSkREBNu2bStz3NnZ2TJt\no1+/fuj1erKzs8tdP3HiRGJiYoiJicHd3b1KYhbqvj2peyjWFzMoJRZyL6B74ju+OqGj32f7af/+\nDgZ/cYAVhy9hNFUwaiyTQfux5kWCeg1qpRowz4muLqLNrnusNsLcqlUrYmPNO/EYjUa8vLyIjIy0\nVnXCAyAuLR8/dwecVTZWradtExfiUvOhbcObB+9hVMEaVq5cyYwZM3jzzTctx3x9fbl06VI1RiXU\nFllZWdjY2ODq6opGo2Hnzp28/vrrZcpcu3YNT09PZDIZR44cwWQyUb9+/dvcURAq14azq2goyemY\ncoSsRxcQtd7EhayzdPJxI6xNQ+LS8nlrbTwb466y+N8dcFH/5d+Btk/BqRNQkoOdsxcXu7+Czs6F\nxo6Nq+V5RJtd91TJlIxdu3bh7+9Ps2bNqqI6oQ6SJInY1AK6WyGd3F+FeLuy/XQGpopGMqpJdHQ0\nW7duLXMsMjKS6OjoCueiCsKt0tPTGTNmDEajEZPJxIgRIxgwYACLFi0C4LnnnmP16tV89dVXKJVK\n1Go10dHRYmGgYF2SBJcOkH3wc/7QJTC+UENWn0X031kfo6mU5U93IryF+59FJX4+lsZba08x+n9H\niH7mIdS2ipv3cnQHGzWU5CJzaoxaqUZj0FTTg4k2uy6qkg5zdHQ0Tz75ZFVUJdRR165ryS7SEWLF\n6Rg33Nhyu7QGZMooKjLPybt48WK5c/Pnz7f8d0RERFWFJNRCISEhnDhxotzx5557zvLfkyZNYtKk\nSVUZlvCgMhrg1E/mTUeunWJzfQ9Mzip69lvG8DWlGE16fn6uC809bqYPlclkjOjQBFe1Dc/+cIw3\nfznJgqjQsl/qbB1BMoLuOmqlmmxNNibJhLwy5zHfgWiz6y6rf4pKS0vZsGEDw4cPr/D8kiVL6NCh\nAx06dBALSITbSrxWCEBAI2er1xX8Z6e8JnSYBUEQ6pSM07CoG6x7Hox6GPgZG5sG06ZBGz4/YEd6\ngYZvxnQs01m+1WNBDXm5V0vWxV5lfezVsieVdiBTgDbfko+5OkeZhbrF6h3mrVu30q5dOzw9PSs8\nLxaQCHcjOdP8rb2Fp5PV63JW2eDn7oDeIDrMgiAIlSb1KHzTGzR5EPUDvHCIRN+HScxPwlsZzo6E\nDF7v05r2zer97W1e7NGcsKauvLfxNDlFt+zoJ5OB2hW0BagVdoDoMAuVx+od5ht5CAXhfiRlFFHf\nwRY3h7tIMVQJQr1dKTXWnDnMgiAItVpBGvw4Ahw9YOJeCBgIMhnrz69HKVOy7XBDOvm6Mb6r7x1v\npZDLmDs0hOtaAwt3J5c9qXIFyYSytAQbhY3oMAuVxqod5pKSEnbs2METTzxhzWqEB8C5zEJaeFb+\ndti3E+TlgtEkoRfTMgRBEO6PJMGGl8CghVGrwbkRAHqTns0XNtNAHoZWp2LOE8HI5Xe30LSlpxMj\nOjRhxeFLXMopvnnCzsk8LUOTj73SnhJ99e/4J9QNVu0w29vbk5OTg4uL9RdqCXWXJEkkZxTRwuP+\np2NklmSy8fxGvj75NWvOrSFPm1dhucA/50pr9cb7rlMQBOGBdnYznN9t3rWvQXPL4f1p+8nV5nIx\nJZDRD/vg535vgyIv92qBUi7no+2JNw/emJahK0CtVGEwGdAb9ZXzHMIDTez0J9R4Gdd1FOoM/3iE\nWZIkDl87zPKE5exP24/EzakWsw/P5q2H3uKJFmXfggQ2cuZIBmj0RpysnPdZEAShzjIZYdd70KAl\ndHi6zKl1yetQSs44mIL4v54t7vnWHs4qJoT7snB3Ms+E52OZsKdyhZIc1H+mBtUYNNgoRDsu3J+q\ny7UiCP9QUqY5Q8a9jjAbTUY2XdjEsI3DeObXZ4jPjmdiyERWD1zNkVFHWDNoDe092/PuH++y5tya\nMte62NuglMvQllbvlAyZTMa///1vy88GgwF3d3cGDBhg1XrHjh2Lr6+vZafOzz//HDDvAJef//e7\nIPr4+FS4Q9yMGTP4+OOPrRKvIAg1VOJWyD4HEW+A4uYYXY4mh31pv1GSG8rLj7bGxf6fdWgndvfD\nRW3Df/fcMpfZ1hFkclR6DTKZrErnMYs2u+4SI8xCjXcu40aGjLsbYTaajGxL2caiuEWkXE/B38Wf\nmV1m0s+vH3Z/rpwGaFmvJV/2+pIXdr7A7MOzaevelub1br4utFHI0FTzlAwHBwfi4+PRaDSo1Wp2\n7NiBl5dXldT90UcfMWzYsDLHtmzZUiV1C4JQRxz8AlyaQsDgMoc3X9iMSTJSz9SFpzo3Q6fTYWdn\nd5ub3J6TyoaxXXz4bFcSL7XzMR+Uy8HOCbn2Onaqqt3ARLTZdZcYYRZqvOTMQurZ21D/LjJkJOcl\n8+TmJ3lj/xso5Uo+eeQTfhn8C5EtIst0lm9QypV8GP4hKqWK+cfmlzlno5BTajBW+45/ffv2ZfPm\nzUD5rDPFxcWMHz+ejh07EhYWxvr16wFISUkhPDycdu3a0a5dO/744w8A9u7dS0REBMOGDaN169aM\nGjUKSbr757t1JOKHH36gU6dOhIaG8uyzz2I0lv9y8cEHH9CqVSt69epFYmJiufOCINRh2clw+Q/o\n+LRldLm4uJiPPvqI+d8txKjx5qXwbkQNH8rgwTc71K+//jq///77XVcztosP9rYKCrWGmwftnMGk\nRy03Z8q4l3bufok2u24SHWahxkv6c8Hfnbbp/fHMj0RtiiKjJIO54XNZM2gNj/k8dsddnuqr6zO+\nzXj2X9nP8YzjluM2CjkSoDVU7yjzyJEjiY6ORqvVcvLkyTLbqn7wwQf07NmTo0ePsmfPHqZOnUpx\ncTEeHh7s2LGD48ePs2rVKv7v//7Pcs2JEyf49NNPSUhI4MKFCxw4cKDCeqdOnWp5vXfq1Kky586c\nOcOqVas4cOAAsbGxKBQKVqxYUabMsWPHiI6O5sSJE/zyyy8cPXq0En8rgiDUeKd+AmQQEmU5JJPJ\nmPXBLLJyrmKve4gAu3w2b95MkyZNACgoKODnn39m27Ztd11NPQdbRnVuiqbUiO5Ge60yJxtQm0yY\nJBN6U9Ut/BNtdt0kpmQINZokSSRlFjEgpNHflllwfAHfxX/HI96P8F6X96ivrn9P9TwV8BTfn/6e\nH878QDvPdgDYKGVIgKbUyMLYTzibe/Z+HqWc1m6teb3T63csFxISQkpKCitXrqRfv35lzv36669s\n2LDBMs9Mq9Vy+fJlGjduzKRJkywN47lz5yzXdOrUCW9vbwBCQ0NJSUmhW7du5eqt6PXeDbt27eLY\nsWN07NgRAI1Gg4eHR5ky+/fvJzIyEnt7845bgwYNuuOzCoJQR0gSnFwFvt3BuRFarRaVSoW9vT3D\nl0xgxx9riZA3o3FDT8aNG8e8efMAcHFx4eTJkzg4ONxTdRPC/Th1OoHswlK86qmZe2w+ZzOOYwI0\nSNgp7FDK76/LI9rsB5voMAs1WlahjgKNnha32SYV4JtT3/Bd/HdEtYpiWudpdxxRrohaqWaw/2BW\nnFlBtiabBuoGKOVyTDIZWn3152IeNGgQ//nPf9i7dy85OTmW45IksWbNGlq1alWm/IwZM/D09CQu\nLg6TyYRKpbKcu3WeoEKhwGAwcK8kSWLMmDF8+OGHf1vuTm8FBEGoo9JiIC8Fur+GXq8nIiKCHj16\n8N6s9zha9DtZvxTwR5Ov8Zw0hsWLFwOQm5vL6NGjefrpp4mMjOTMmTPMmzePxYsXY2v791PyPJ1V\nnLdRkFdSiqfzn22cXIncWIpMJsckVW07Ltrsukd0mIUaLekOW2LvTd3L5yc+p79f/3/cWb5hWMth\nLE1Yyvrk9TwdbE5/pLJRoNEb72pUwZrGjx+Pi4sLwcHB7N2713L88ccfZ+HChSxcuBCZTMaJEycI\nCwujoKAAb29v5HI5S5curXCu2v149NFHGTx4MC+//DIeHh7k5uZSWFhIs2bNLGW6d+/O2LFjeeON\nNzAYDGzcuJFnn322UuMQBKGGOrkKlCoIGIgkSXTr1o127dqxMn4rJkUJ4+fMY3qvgZSUlLBixQo2\nbtzIoUOHyMvLY8iQIVy5coVTp06xefNmzp49S0hIyB2rdFQpMUkSuSWl5ja7tBiyz3FB5YBMYYOv\ny513Eawsos2ue0SHWajRkjJupJQrP8KcWZLJW7+/RYBbAO91ee++OssAPi4+BDcIZselHZYOs9pW\nQW5xKZIkVes3b29vbyZPnlzu+DvvvMOUKVMICQlBkiR8fHzYtGkTL7zwAkOHDuXnn3+mR48e9/x6\n804CAwOZNWsWjz32GCaTCRsbG7744osyjW+7du2IiooiNDSUZs2aER4eXqkxCIJQQ5lMkLAOWvYB\nlTO2YJmCEPpaD0z+zgz2a03//v1JTU3F09MTW1tbIiIiGDp0KAkJCQwYMICMjAzOnTuHq6vrXbXB\nNgo5dnZKcopKaeBoh9zGHmQK1BLkG7RV2o6LNrsOkmqQ9u3bV3cIQg0z7ZeTUsiM7ZLJZCpz3GQy\nSZN2TpLaL28vpRSk3P0NdcWSFL9WknbNkqR98yQpeZckGfSW09+e+lZq830bKa0wTUpISJByinRS\nXGqepC01VNYjCXVAQkJCuWM1uf3SaDRSx44dpZCQECkwMFCaPn16uTImk0l66aWXJH9/fyk4OFg6\nduzYHe9bk59ZqEapMZL0rrMkxa2SvvrqK+no0aOSJEnSLzs2S4AUPKa3tHnzZsnLy0tq3LixNGvW\nLPNlqalSUFCQJJPJJGdnZwmQBgwYIGk0GikwMFD69ddf/7bahIQEqaCkVIpLzZPyinXmgznnpbyM\nU1J8Vryk1Wut+thCzVUZbbbIkiHUaEmZRbTwcCw3KrAvbR970/byUthLNHNudpur/+LsFljYDn4e\nA7/Ng92zYHkkfB4GcatAkujdtDcAOy/tBEBlY/4Tqe5MGYJwP+zs7Ni9ezdxcXHExsaybds2Dh06\nVKbM1q1bSUpKIikpiSVLlvD8889XU7RCrZe0HWRySpt2Z9asWXz11VcAbCyKo/G4xrRRNePnn3/G\n09OTa9eukZubC8B3333H6dOnmTJlCrGxsfTr149evXrRt29fEhISSEtLu2PVTioldko52UWl5gN2\nzqiM5jm/VZmPWah7RIdZqLEkSSIpo7DchiV6k55PYj7Bx9mHpwKeurubxXwH0U+Bgzv8ex28kw1v\npsGIZeBQH9ZOhJVP0kTpgL+LP79fMecAtVMqAGrEwj9B+KdkMhmOjua/I71ej16vL/cldP369Ywe\nPRqZTMZDDz1Efn4+6enp1RGuUNud2wbenbB1bUhiYiJz5syhRKPh0KVNpC9NZ+Xib3B1daVHjx5M\nmDCBl156iatXrzJv3jyefPJJ5syZg6+vL7m5ubzyyit06dKFVq1aMWTIkDtWLZPJqO9oR0mpgWKd\nAeycsJMk5MjQGEWHWfjnxBxmocbKKS4lr0RP879sif1T4k+kXE/hvz3/i4389tup3sg3Oa57M+w3\nvwIteps7yDZqcwGFDQQOhtYD4fAi2DEd/teHLqF9WXVxE5K3hEIuw1YhRyc6zEItZzQaad++PcnJ\nybz44otlcsMCXLlyxZILF8xzMK9cuUKjRrdP6SgI5RReg/Q4pJ7vIMO8892FCxfo1jMC5+H2KBQK\nfPx8WLBgQblL58yZw+DBgy0ZMezs7FAqlSxdupT09HRWr16NSqVi165dfP/997cNoZ69LRnXtWQX\n6XCo74BMYYeKqt0iW6h7rDrCnJ+fb9mdJiAggIMHD1qzOqGOSfpzS+yWt4wwXy+9zqK4RXRu1Jnu\n3t3/9vqYmBgmT56MzaaXwCMQhn13s7N8K7kcHn4B/r0Wrl+hS+wvlJpK0Rl1gDlThpiSIdR2CoWC\n2NhY0tLSOHLkCPHx8WXOSxXsHlbRAqklS5bQoUMHOnToQFZWltXiFWqppF8BWBaro1u3bmRkZPDK\nK69QoitG1ciVZ559lhdeeAFJkkhPT2fIkCGWnMMvvviiJd8wmHMWp6amMm/ePPr27cvEiROZNGkS\n+/fvp6io6LYhKOQy3Bxsua4xUGowgZ0TapMB7Z8L/wThn7Bqh3ny5Mn06dOHs2fPEhcXR0BAgDWr\nE+qY5MwbGTJujjD/eOZH8nX5vNr+1Qr/Md+3bx+//fYbAM888wypi5/k5KU8/mj6IrM/+RydTnf7\nCn3DYcwG2hcXYiuBzqgFwM5Gjs5gEg2tUCe4uroSERFRbic1b29vUlNTLT+npaXRuHHjctdPnDiR\nmJgYYmJicHd3t3q8Qi1zbjs4e6P2bI6rqyvu7u54NPXGUKxD96uJ40dj2LZtGzKZDJPJxPHjx0lI\nSKjwVra2tnh4eBAZGUlSUhJOTk44OTkxbdo0yxSj26nvYM5dnFOsAzsnVCZzG35jIEQQ7pXVOszX\nr1/nt99+4+mnzem5bG1tcXV1tVZ1Qh10LqMIJzulJQl9sb6YH878QESTCALql//yJUkSb775JlOm\nTMFkMmGfd5ZGqRt47bAb4155j3feeYe1a9f+faVe7VH/6xfa6ErR6zVgMmGnVJgbWoOYliHUTllZ\nWeTn5wPmHb527txJ69aty5QZNGgQy5YtQ5IkDh06hIuLi5iOIdwbowEu7ofmPRkRFcU333zDtGnT\n2BvzO5hgwCP92bZtm2X3Oy8vL5KSku44NzkrK4uUlBRcXFwoKiqiZ8+eREdH/+1ba1ulHGe1ktzi\nUky2jqj/HPAQ0zKEf8pqHeYLFy7g7u7OuHHjCAsLY8KECRQXF1urOqEOSso0L/i7MZIcfTaaAl0B\nz4ZUnEhdJpOxefNm1q1bR0pKCtqt00HtxpS3P0Qmk/HZZ58RFRXF9evX/75ir3aE+fZGj4Qp/5Il\nU4auGqZl/HUU5fvvv2fSpEmAeWcomUxGcnKy5fyCBQuQyWTExMQAUFRUxLPPPou/vz9BQUF0796d\nw4cPV90DCDVCeno6PXr0ICQkhI4dO9K7d28GDBjAokWLWLRoEQD9+vXDz8+P5s2b88wzz/Dll19W\nc9RCrZMeC7oCzslaEBMTQ1hYGJ988gmqvs40G9uWz979gOXLlzNlyhROnDgBlN3F7naaNm1KYmIi\nzzzzDAaDgRdeeIFRo0bx+OOPo9HcvgNc38EOo0kiX2vC1sYeOdbvMIs2u+6y2qI/g8HA8ePHWbhw\nIZ07d2by5MnMmTOH999/v0y5JUuWsGTJEgAxH04oIzmziEdbewJQoi9hWcIyujbuSpsGbcqVjY+P\nJyAggHr16pmTwTdrQlO1lvi1C+gW+BiNGi2iSZMmDBs2jMuXLzNkyBBef/11lMqK/wTCAoZjuGZA\noytAbecEKNHqTbhUMAW6OgUHBxMdHc3bb78NwOrVqwkMDLScnzBhAr6+viQlJSGXy7lw4QJnzpyp\nrnCFahISEmLpoNzqueees/y3TCbjiy++qMqwhLrmwl5KjRJdxr5Ht/Bw6tevT3ZONqUFmTTThdC2\nbVsOHjxIhw4dCAsLu6db+/j4MH36dGxtbXnrrbdQq9UEBwejVt++UXawU2CnNG8+5aZyQq3NRlvN\nI8yiza69rDbC7O3tjbe3t2Ul9rBhwzh+/Hi5cmI+nFCR3OJSsotKLSnl1iWvI1eby8SQieXL5ubS\nrVs3y65KTk5OeLva0sBRgdRuDCqVigMHDnD06FFat27NsWPHePvtt5k5c+Zt62/r3haAEhsV8utX\ncFCYamSmjCFDhrB+/XrA/FbHxcXF8nd0/vx5Dh8+zKxZs5DLzX/qfn5+9O/fv9riFQShDru4D5lH\nIAv/+1+GDRtGfn4+kkJGzo48zu89Qc+ePXFxceHhhx/+x1UcOXIEhUKBn58fO3fuJDk5ucIvg2D+\nEujmYEtJqQGdwh6VJKE1aDFJ1deWiza79rLaCHPDhg1p0qQJiYmJtGrVil27dpX5FiUIf+fGltjN\nPRwxmoz8cOYH2rq3pZ1nu3Jl69Wrx/Dhw9m2bRs6nY7slDNcy84nTWaLTO1C+oUL9O7dm2bNmjF2\n7FiKi4u5evWqpREyGAzIZDIUCoXlnq4qV5RyJSU2KtDraEwmqQavqnn4W2g0GkJDQy0/5+bmMmjQ\nIMvPzs7ONGnShPj4eNavX09UVBTfffcdAKdPnyY0NLTMcwmCIFiFXgOXD1PQ8ilWrlh6mL3aAAAg\nAElEQVTJtm3bmPzaf1iy/SsauPvwuM/DFaaSu1f/+9//GDx4MPv372fBggW8/fbbSJJ024WD9ext\nzCnmSpU4ShISoDPqUCut87pQtNl1l1WzZCxcuJBRo0YREhJCbGws06ZNs2Z1Qh2SlHkjpZwTe9P2\nklqYyujA0RWWlclkuLm5kZ+fj7e3N29MGkeeFmQKGzZs2ED79u3ZsmUL69evR6lUMmXKFPr27Uts\nbCxffvkl7dq1Y8SIERgMhjL3tVXYojFokZy9UEsaxgx5zNKw6fV6IiIi+OGHHwAoKSkhIiKCVatW\nAVBQUEBERAS//PILANnZ2URERLBx40YArl27dle/B7VaTWxsrOV/FY2Kjxw5kujoaNatW0dkZORd\n3VcQBKFSpR4m87qGScti2bhxI/7+/iSYMvGa0Ii+D/Vh/vz52NjcPm/+3XJ1dWX27Nl89tlngDmh\ngJeXF82bNy9XNiIigh+WL8NFbUNmgYaBQyey8eeNaAwa0WYL98yqG5eEhoZaJrILwr1IzizCwVZB\nIxcVbx5chpejFz2b9ixTJiEhgenTp9O/f39ycnKwt7fHaDDgobvIzy91JmL6JsuuZUFBQUydOpXo\n6GhefvllMjIycHd3Z9SoUej1egIDA8t9q7eV22KUjJTaOaJQqLDFgMFY86ZlDBw4kKlTp9KhQwec\nnZ0tx4OCgoiLi8NkMlle7wmCIFjFhX1sOGdi1ZZ9BAcHc+7cOc5+eJaGA5vzxcY5jO4TSadOnSql\nqq5duzJ27FiSk5MZOHAgEyZMwMbGBr1eT1paGl5eXmXSjtZ3sCWzoBiQI0dCqy9BpVBVSiz/hGiz\nayex059QIyVlFtLc04mEnASOZx7ntY6voZSX/bhOnTqVXbt20ahRI65evUpeXh4erg7sTb7OgesF\nDK1f37Il8I8//sjMmTPRaDQ0atQIg8GARqPh3Xff5dVXXy2TLP8GW4V5t6kSgwa1Y2P2rVmCVuUB\ngI2NDXv37rWUtbe3L/Ozi4tLmZ8bNGhQ5ueGDRve/y/pT2q1mrlz59KyZcsyx/39/enQoQPvvvsu\nM2fORCaTkZSUREJCAoMHD660+gVBELh0ALsGzeja1Y2CggJahbbh5JFj9Bk+lhenP06HDh0qtbr3\n33+fxYsXs3HjRoKCgli3bh3jxo3DZDLh4eGBra2tpc2VJAlnexUr1qzHJM9Aoy+hsZO3aLOFeyK+\nwgg10rmMIlp4OLLy7ErslfZENi//2mrBggV06tSJ7t27ExISwrvvvsuwMDc+j2zMgi++towwfP/9\n92zfvh17e3vGjx/PsWPHOHPmDMnJyaxfv57mzZuze/dulixZQq9evSgoKABAKVeikCso0Zdgo3am\nQLLHVpsNRn2V/i7uxsiRI2nXrvz87m+++YZr167RvHlzgoODeeaZZyrcjEIQBOEf02s4EXOE51Yk\nk5GRweHDh/F+pgPez/vwdr9nK72zDDB8+HAuX77Mo48+SrNmzVi2bBkajYaAgADL1to33Fj8V2Cw\nQSVJ6Ez6al34B6LNrpWkGqR9+/bVHYJQA+QV66Rmr2+SPtsdK7Vf3l6a+cfMMue3bdsmZWZmSps2\nbZI8PT2liIgISS6XS20CAyRpZgNJ2vrGbe+9cOFCafTo0ZJOp5P69Okj2djYSIAUFhYmubu7S82b\nN5diYmIkSZKkhIQEKaUgRUrKS5IkSZKSr2ZLpivHJSk/zXoPL9QKCQkJ5Y49iO3Xg/jMQgUu7pf+\nr5ON5OVZX5LJZJKPr48U+FWY5OTvIS1fvtxq1WZkZEiDBg2SfH19JUA6fPiwJEmSZDKZpMLCwjJl\n9QajdDItX8q+liDFZ8VLxaXFVotLqHkqo80WUzKEGif5zwV/ObI/0Bl1jGg1wnLu4sWL9O/fn4cf\nfpiEhATy8vLIzMxkwIABbN60iaRMe1q0GXbbexcUFHD9+nXkcjlDhgzh0KFDdOvWjVmzZqFQKGjZ\nsmWZ0Qm1Uk1RSREmyYRMaUeRwRGnkmxw8gS5+PMRBEFIP76dhCwTGTn5+Pr6cl1fDCnQxMMHJycn\nq9Xr4eFBamoqJSUl+Pn5YTQaMRqNZGRkcPXqVYKCgix5mpUKOc4qJXqdChQlaPTF2NvYWy02oe4R\n/+ILNY45Q4bE0ZwthLiH0MqtleWcr68v33//PWfPnqVv376oVCo8PDwYNmwYO958hBY+OvAq/5rr\nhrfeeguj0YhCoeBf//oXS5cuZdiwYbRo0YJevXrRr18/3njjDctOTDcWhmgNWuxsFGSWuuAkK4KS\nHHD0tOrvQRAEoTZ4ZubX7Lts5MeVPwEw6ul/4STz5uieA9jbWbeb8eGHHzJ69GjCw8PRarWcOXMG\nnU5H48aNy+0iWM/eliyNGqVUjLa0COzF3g/C3RNzmIUa51xGIfbOl0gtSmFEy5ujyzfSvh0/fpw5\nc+bg6+vLO++8w5YtW7ArzWOg6zkIHg63rI6uiEKhQK/X07dvX5o3b46LiwshISHEx8ezcuVK+vfv\nzyOPPIIkSZZcnRqDBjulnGLJFpOtIxRlQTXPgRMEQahu+bk57IzPwKu+E4cPH6ZVeBuavtqEIJ++\nVu8sA4SFhdG1a1ciIyORJAmZTEajRo1o2LBhuUwTjiolpXI1KklCY9RaPTahbhEdZqHGSc4swsXj\nBE42Tjzu8zhgnkrRqlUrfvzxRw4dOoTRaCQmJoaSkhLi4+ORJawzd2CDbz8d41Y2NjYMGDCAAQMG\nsG/fPs6fP0/79u3Jy8sjKCiIRYsWmTczkSlQyBVojVrslOY/F51dAzDpQZNntd+BUHNJklTdIQhC\njaG5dByDCa7klrBw4ULm7/8f6T9e4/T8n6vkb8XDw4M1a9YwevRotFqtpdMsl8vJyckhMzPTUlYu\nk+Fib4tCUqCTTBhNRqvHJ1S/yvocig6zUOOcy8xBYxPHYz6PoVKap0QUFhYSEhJCRkYGBw8epGvX\nrsydO5cNGzawe/duOPUzNAwG91Z3uPtNr732GiNGjMDe3h4bGxvWrFnDxYsX6dKlC61bt0alUpGb\nm4tKobKMMAOUyOxBqYLiHKs8v1BzSZJETk4OKlX15XAVhJoiNTWVQU9NoLGTjH6PPYqTkxObFy3D\ne3gPvvz88zK5kK1JJpMxe/Zs5HI5MpmM3NxcSkpKuHz5MllZWWU6TK72Nkgm8zoVrb6kSuITqk9l\nttliDrNQo1zX6smRTqBGS3+//pbj3t7eqNVqPv74Y3766SdWr17NyZMnGThwIORegCvHoHf5HZXu\nhr+/P/b29iQmJhIfH89LL73EyJEjefjhhwkPD6dQX0hxaTE6h1IyC7SUZCrJlGtAkw8ZWlDc/+5V\nQu2hUqkqzNstCA+axYsXc+7SVf6Y5EeLWRt56cMp7DRu59HQUfR5/LEqjeXUqVPMnj2b1atXk5eX\nR1FREcXFxdSrV4+zZ8+WKZt7vQCtvJgS5XUcVa5VGqdQ9SqrzRYdZqFGScoowsblBK627rT3bA/A\n9u3badGiBevXr0etVjN79mxiY2M5e/YscXFxcGqN+eI2Q/9RnX369GHdunW8+eab7Nu3D4CffvqJ\npUuX8sUXX9Cqfyum7J3Cin4r+Gh7EU3c1Hwz1A/mt4aHnofHZlXKswuCINQm+fn5KCQTHT5NYcVD\nmzjf6Br5q7QMHNCmymN5++23efHFFxk3bhzHjh1jypQp9OzZk549e1qmadyweFc8P6eMJ0TdhPlP\nba/yWIXaSUzJEGqUuKtpKByS6NWkL3KZHK1Wy6hRo3jzzTextbWladOmrF69msWLF7N27VqQJDj1\nEzTrCi7/7Btk48aNWbduHSqViuDgYL7++mteffVVjh49ygsvvEBg/UAAzuScwc/dgQtZxeDoDi37\nQFx0jdzIRBBulZqaSo8ePQgICCAoKIjPPvusXJm9e/fi4uJCaGgooaGhzJz5z97YCA+G8+fPc+j3\nveRpTSCTcfjkYc6djCHvtwxauFX9lCVvb2+Cg4NxdnbG29uby5cvM2rUKDZu3IiHhwfnz5+3lB3Y\n3p/GWhvOaK5VeZxC7SU6zEKNsi9tBzKZiaiAQYD5Vco333xDYmIijRs35umnn8bf35+JEyfi5+cH\n105B9rm7Xux3O5IkceHCBQoLC3FycmLgwIFERUURHx9PQ4eGuNq5kpCbgJ+7A5dzS9AbTRD2byjO\ngqRfK+PRBcFqlEoln3zyCWfOnOHQoUN88cUXJCQklCsXHh5ObGwssbGxTJ8+vRoiFWoDk8lEREQE\n9ezgX22U+Pv6kKbKwLlDPV77YTPNmzevtti6dOlCcHAwHTt2ZMKECaSlpZGdnc327TdHkhu7qqmH\nN2lKE9cL06stVqF2ER1moUY5V/wHNsZGtK5vXryn1Wp56qmniIuLIyAggMmTJzNgwICbF5z62byB\nSOCQ+6pXoVCwdetWGjVqxNKlSxk4cCDFxcW88847vP/++wTWDyQhJwHfBo4YTBKpuSXQvBc4NoQT\nP9xX3YJgbY0aNbJsw+vk5ERAQABXrlyp5qiE2io1NZX09HT0xXnMH9KQo7FxJDU8j7GoJWO6P1yt\nsXl5edG0aVPWrFnD4sWLGTduHJs2beK5554rU65Vo64A7Dm6qjrCFGohq3aYfXx8CA4OJjQ01Cp7\nyQt1S742nyKS8LLtCMDChQuJiorCYDAQERHBwoULCQgIYNSoUeYLTCaI/wX8HwV7t/uu39/fn59+\n+omdO3ei0+nIycnh1KlTpKamElg/kOS8ZLzdzNP+L2QVg0JpHtlO3mleACgItUBKSgonTpygc+fO\n5c4dPHiQtm3b0rdvX06fPl0N0Qm1gVqtxtXVlX2nr+L/cTp7Luzl1IwYijbk07qh9Xb2uxvPP/88\nX375JYmJiZSUlPD000+zdOlSCgsLuXr1qqVcv65PAnDswt5qilSobay+6G/Pnj00aNDA2tUIdcCO\nlL0gM9GuQTcAvv32W5KSkmjbti2XLl3C09OTU6dO3bwg9RBcT4NeMyotBqVSiZOTEyNGjECr1TJ7\n9mzOnz+Ppr4Gg2QAG/OctwvZRYAnBEXCwf9C4lYIfbLS4hAEaygqKmLo0KF8+umnODs7lznXrl07\nLl26hKOjI1u2bGHIkCEkJSWVu8eSJUtYsmQJAFlZWVUSt1BzXLt2jY8//picHHNazXEDurL2wmYc\nAurRs32fKksl93fkcjlffvklf/zxB02bNiU5ORkvLy9atWrFsWPHAPDx9MXTIONKaQpGk4RCXv1x\nCzWbmJIh1BhbL+zCpHeia5NQAPr3748kSfj6+pKXl2fOt3yrUz+DjT206ltpMXh6evLkk0+i0WjY\ntm0bo0aNok+fPngYPQC4XHwONwdbLmYXmy/wag8uTeD02kqLQRCsQa/XM3ToUEaNGsUTTzxR7ryz\nszOOjo4A9OvXD71eT3Z2drlyEydOJCYmhpiYGNzdxdbCD5ovv/ySTz75hF3fzuDQ02pmzJ3BkZw/\nqN97MO9Nee7ON6gily5dYtmyZcyfP5/hw4cTFhaGra1tmZzM/jbuXLHVcST56t/cSRDMrNphlslk\nPPbYY7Rv394yIiEIFSk1lhKXcxhDUSAtPRw5cOAAc+bMwWAw4OHhQWlpKUbjLbsyGfVwep25s2zn\nWGlxyGQy/vvf/zJjxgx0Oh179uzBzc2NHh164CA5kJCTgF8DB85nFd+4AIKGwPndYlqGUGNJksTT\nTz9NQEAAr7zySoVlrl27ZulMHDlyBJPJRP369asyTKEWOHXqFEqlkhWr1tDQ1YGlF05QfLEQX1UE\nPg0cqjs8i6lTp/Lrr7+Sl5dH3759ef/991mxYkWZEfD2jdtzxUbJ4YMbqzFSobaw6pSMAwcO0Lhx\nYzIzM+nduzetW7eme/fuZcqI13sCwJFrRyg1aZBrAhnWtyfHjsUQHh4OwFtvvcX8+fOxtbW9ecH5\nPaDJheDhVoknMzOTgoIC/P39ycjIoE+fPqgcVX8u/ItkT+Itn9XASPhjISRugdCnrBKPINyPAwcO\nsHz5csuaEoDZs2dz+fJlAJ577jlWr17NV199hVKpRK1WEx0dXSNerws1y8GDBzEYDCzbdQo7Q1O2\nJX7Jxa0XeHGtf3WHVoatrS1dunQhMDCQwsJChgwZwiOPPEK/fv149tlnAQht8Thc2Ur6tV3oDM9g\np1RUc9RCTWbVDnPjxo0B817vkZGRHDlypFyHeeLEiUycOBFALAx8gO1N3YtcssPHLgB10yZoNCUc\nO3YMe3t7nJycynaWwTwdQ+VqXvBnBS1atMDd3Z2BAweycuVKUlNTaZHYgqSmSXT3tiP7mI7rWj3O\nKhvwagcuTc3TMkSHWaiBunXrVuZVdEUmTZrEpEmTqigioTb6/PPPcXZ2xqDX8/uTpaR1fpy9xb/T\nqMFIRnYPqu7wKjR58mQmTJjA9OnTOXbsGM899xy9e/fGz8+PgEadAFDYXGRfYhaPBTWs5miFmsxq\nUzKKi4spLCy0/Pevv/5KmzZVv/uPUDv8fuV30LQguGljevXqRVJSEpIkkZ2dzcGDB8sW1hXC2U3m\nqRBK24pveJ/q1atHXFwcc+fOJTAwkKSkJC79cQldsQ61QyYAF8tMyxhsnpahLbBKPIIgCNVJkiQ+\n//xz1Go12YdW0bqBnMOeSpQqFR06jqORi7q6Q6zQkCFDsLOz48cff0ShUDB8+HCUSvNYoZOtE34K\nR3LV19kYe7maIxVqOqt1mDMyMujWrRtt27alU6dO9O/fnz59+lirOqEWSy1M5UrRFXIT1KQf2cyM\nGTNwcnLi3Xff5bfffqN3795lL0jYAPoSaGvdrBSenp58+umn7Nmzh/z8fPZv2c+16Gto5ZeAG5ky\n/tSqP5gMkLzLqjEJgiBUh4ULF5KSksKZM2f41/OvEp8tMX/6TxTEudM/yK+6w7stNzc3nn32WZKS\nkti5cycmkwkHh5tzrdu5teaknQ3XzhykSGeoxkiFms5qUzL8/PyIi4uz1u2FOuRw+mEAsn7ZS3TW\nD7i6uJCbm4uHh4dlHnMZcSvBzQ+alM8jW9kiIiJwdnbGxcUFV1dX4g/Ec+HaSeSyiJsjzABNOoHa\nDc5tgzblMxAIgiDUZocOHcJoNFKvXj02/pFAu9AWXE9KwrZlUx6v4VMZPvroI65du2bpNA8ePJh5\n8+bRpUsX2vn0ZnVWDH42R9kef42h7b2rO1yhhrqrEeahQ4eyefNmTCaTteMRHkCH0g/hqKhP/UHT\nGBI5jKKiIuzs7CyLk8rIuwQp+82jy1WwIKlTp06sW7eO3bt3M2HCBGTIiD1znCZu9pzPvqXDLFdA\ny8fN22QbxSiFYD2iPRaqmk6n4+TJk3Tq1Ilvlywic6orGR2bEjg3jOCwJ2tUdoyK2NjYMHjwYNLS\n0njttdc4cOAAO3fuBCCsiXldlYvTedbHifRywu3dVYf5+eef58cff6RFixa88cYbnD171tpxCQ8I\nk2TicPphXGWB2ORc5Pff9qDVann00Ucr7jCf/HMb05CoKouxR48erF69msmTJ6N2UnP25FmauEjm\n3f5u1bIPaPIg9XCVxSY8eER7LFQlSZKYOXMmSUlJ9OnTh0HtvbhSrGO3NhNdUTB929SOEdmkpCSy\ns7OZPn06Xbp0sewY6+XohYfMjlxVDgeTM8kq1FVzpEJNdVcd5l69erFixQqOHz+Oj48PvXv3pkuX\nLnz33Xfo9XprxyjUYYm5iWRlZHF8wR9k7f4OuVxOv379WL9+ffmUVpJkno7hEw71mlVpnFu2bAGg\nOK+YjPUZbJ01lgtZ1zGZbsk84N8T5DZwbmuVxiY8WER7LFSlI0eOMHv2bEpLS9mxYwf9o8bT68cS\nEj9PRn+9bY2fjnHDpEmT6NKlC2BOG/r222+j1WqRyWS0c21OnJ2CllIKW06lV3OkQk1114v+cnJy\n+P777/nmm28ICwtj8uTJHD9+vPyCLEG4B4fSD6FN1ZIZd4aSnHTy8vLw9PS0rGIu49IByL1QLanb\nVqxYwbx58+g7qC/1B9TH2cMZTYmW9Ovam4VUzuDTDRK3VXl8woNFtMdCVfHz88PNzQ0ALy8vQj0k\nWvVvjHu4N41VQQQ0cqrmCO+Om5sba9euJTIykry8PI4cOcLgwYMBCGvyCNeUSiLqJbA+9ko1RyrU\nVHfVYX7iiScIDw+npKSEjRs3smHDBqKioli4cCFFRUV3voEg3Mbh9MMEdQnBPfItHF3NjfLcuXMr\nLhzzP1C5QOCQKozQrEmTJkydOpUZb80gf1c+V88mI5PLuZD1l89/q76QkwQ556s8RuHBINpjoSod\nPnyYvLw8nn/+eb79+mve6FJMZjdXbH260yeoUa3a3Eaj0XD16lUiIyO5cOGC5YtAu2Y9AGjgnMjx\ny/lczimpzjCFGuqusmRMmDCBfv36lTmm0+mws7MjJibGKoEJdZ/BZODYtWMEq8LJ3vgRaiXY2dnR\noEGD8oWLsszp5DpOAFv7qg8WKCoqomfPnpQWlyK3laPLusThuAaEt3C/WahlH9j6GiRuhS5iEwih\n8on2WKgqmzdvJjIyknr16tGzZ082/biYQ8cK0PV1RlcQQp82tWM6xg1ubm6kpqZy+LB5nUmPHuaO\ncgvXFjigINWUhgwTG+KuMKlni+oMVaiB7mqE+e233y537OGHH670YIQHS2JeIuf/d57VLy5F0pfi\nYG/P119/XfGIRewPYNJDh3FVH+ifHB0dadu2LbZqW0ylJjKWv8rPSxeXLVSvGXgEmTvMgmAFoj0W\nqspHH32E0WjExsaGESNGMOujT1lzTIdK5oybsjlhTepVd4j3xMHBgX379uHr60vLli159tln+e67\n71DIFYQ6NeWEDUR6FbIu9uodd8YUHjx/O8J87do1rly5gkaj4cSJE5YP0PXr1ykpEa8shPtzIuME\nKi8V+bFaMJYS0Lo1kZGR5QuaTBDzHTTrBu6tqj7QWxw4cICfjv7EtB3TyFpsxN63XflCrfrA75+a\nM2aoa9c/KELNJdpjoap9+OGHDBo0CK1Wy7fffkvnoo2MkiWgK2xDn5aeyOW1ZzrGDb6+vmzbto3m\nzZvTokULxo8fT7t27ejgHc5nhRd50TmJX064cCa9kMDGztUdrlCD/G2Hefv27Xz//fekpaXxyiuv\nWI47OTkxe/Zsqwcn1G3HM4/TIrwF55McuHJkK126dEGhUJQveH4X5F+CR6dXfZAV6NayG6mDUylN\nL+V88rnyBVr2hf2fQNJOCBle9QEKdZJoj4WqdPr0aebNm0d2djaLFi1ixPDhHP3uIwxONpRcDuSR\nR9zvfJMa6tVXXyUoKIjTp0/TvXt3AgICIF+CM8vQGWJQyjuyPu6K6DALZfxth3nMmDGMGTOGNWvW\nMHTo0KqKSXgASJLE/pj9yI7JuXLkN5Q2tri6ulZc+OB/wakRBAyq2iBvY9X/VlGaXgrAld9+ZvYc\nP6a98drNAl7twb4BJG0XHWah0oj2WKhKI0eOJD7+/9m77+goq62P499nSnqvpBFCCukJkJAghFBE\nSKiCoIgIV6SpoNf6il712hsiF1REAQUvqBcUpApKCSIhBEiBAAk1vfc+7f1jNIggoiQZkpzPWiwX\nMyczvyzDw+HMfvY+wfjx49m4cSP/fukF7nvcBBMre+rqvYjx6bgb5ri4OObPnw9AY2MjZ86cITAo\nCDNkHK85R4yPPd+l5PP0CH/kHfAUXWgb190wf/HFF9x3331cvHiR995776rnf3vKIQh/RfqldJKf\nSUYmyQCJ6GGjWi5gVyhMh/P74PaXQGHUviH/wPz589mYvpHDGw+D0oKlS5fy9JOPX26FJ5OB7x1w\nZrt+6p+8zSbQC12IuB4L7aWiooLCwkIkSeLEiRPk5+fz5LSR7LE/hXWTL927O2JtpjR0zL9tzpw5\nVFRUsHfvXn788Ueee+45nnnmGfpYeJLUnMljvTQ8kNnIoXNlDPS9xk3oQpd03Zv+6ur0k8xqa2up\nqam56pcg/F1n6s7gcr+LfvCHXMH8Rx/FzOwa3S8OfQBKc+g7o90z/hGFQsHDTz+M33t+yIwVGJlZ\nXN032m8ENFZC7hHDhBQ6nZu5Hufk5DBkyBACAgIICgpiyZIlV63R6XQsWLAAHx8fQkNDOXbsWJt8\nH8Ktz8rKipUrV+Lj48PYsWNJT09n9HAzKuVyLpWEMdiv454u/+qf//wnzc3NeHt7s3fvXjZv3kw/\n9xguGCnx5yiWJgo2Hss1dEzhFnLdo685c+YA8OKLL7ZLGKHrOFl1ElmVDEsbB2qqKwn39bh6UXUB\npG+AyJm33M1zYY5h5K7IpTm/mko7J7RaLTLZb/796T0EZArI3AmeooOBcPNu5nqsUChYtGgRffr0\noaamhr59+zJ8+HACAwNb1uzYsYOsrCyysrI4fPgw8+bNa2m/JXQdWq2W8PBwLC0tycrKora2FkdH\nR/5Xno5SCTW1/sT26vgb5g0bNrBv3z5kMhk2Nja8/fbbnCw5AafXkJK7l9Ghg9l0PI9XxquxMBaf\nEgo32Fbu6aefprq6GpVKxbBhw3BwcOCLL75o62xCJ1VaWsqmdZtoOtGEWqfDslsPeni4X70w6WPQ\naSB6XvuH/BN+tn405+rrmKvLiwkNDaW8vPzyAhNr8LwNMr83UEKhs/o712MXFxf69NF3dLG0tCQg\nIIC8vCsnmm3evJn7778fSZKIjo6msrKSggIxJrirSUtL49SpUyQlJeHt7c3q1aupLb5EgtSIl8YB\nezNLgl2tDR3zpt1555307dsXmUyGXC7n1Vdfxd8+AEvkJFVmcldfNxpUGjEqW2hxQxvmXbt2YWVl\nxdatW3F3dyczM5N33nnnht5Ao9HQu3dvRo8efVNBhc7jf9/9j9QPUinNKqWhspTRD72IkdHv6pOb\navWT/QLGgG0Pg+S8HoVMwcSlE/GaHY5H9BjUajX5+flXLvIbCSWnoOKSYUIKndQIiSQAACAASURB\nVNLNXI8BLl68yPHjx4mKirri8by8PDw8Ln/S4+7uftWmWuj85HI5CoUCjUaDTCbjlVdeoanqCNlK\nJY1VvRjk59gh28n9npmZGatWreLll1+mvLycLVu2MOmuSfS16M4RuZo+VjV4OZiz8agoyxD0bmjD\nrFKpANi+fTtTpkxpGSd5I5YsWaJv2SIIv/Ab5oddnP5nyMjVnyEDo69edPwLaKyC/te4EfAWEdkj\nEovbdFQ36e+yrq6uvnKB7wj9f7N2tX84odO6metxbW0tEydO5P3338fK6sqWWdca1HCtIUIrVqwg\nIiKCiIgISkpK/mJ64VZWUlKCQqHg008/JTQ0lOXLl/PMM89w4KL+k7KsiihiO0H98q8CAwMpLCzE\n3t4eExMTJEmit3M02UolRVk7mdDbjcMXyskpF33OhRvcMI8ZMwZ/f3+Sk5MZNmwYJSUlmJiY/OnX\n5ebmsm3bNh588MGbDip0HgezDlKxuwIjYxOQZAT+/uM9rQYSPwSPKPCINEzIGxDpHEnl0XKqju9G\nkiSSkpJobGy8vMDBB+y89XXMgtBK/u71WKVSMXHiRKZOncqECROuet7d3Z2cnJyW3+fm5uLq6nrV\nutmzZ5OcnExycjKOjp1n8yTA4sWLCQwMZOXKlaSlpVFbWwtAQlUm3dVyVGonYjpR1wi5XM727dsp\nLy8nISGBl156idv8xwNw5NIP3NnHDYBvjolPWoQb3DC/+eabHDp0iOTkZJRKJebm5mzevPlPv+6x\nxx7j7bffvvJmqN8RpxVdy1dffcVnb32G0kyJvYsHVn3HEODyu+bwp7boB5X0f8QwIW9QH+c+WPlZ\nI7M0Q6fT8dRTT11dS+o3Ei4cgOY6w4QUOp2/cz3W6XTMnDmTgICAP2w/N3bsWNasWYNOpyMxMRFr\na2tcXFza4lsQblHdunUD4MyZM8hkMtzd3amrLSJZasa9yZlQN2vsLYwNnLL1SJLEww8/jCRJODk5\nMWXKFOxxxEorI6nyDO62ZvTvac83x3PFqGzh+l0yfuvUqVNcvHgRtVrd8tj999//h+u3bt2Kk5MT\nffv2Zd++fX+4bvbs2cyePRuAiIiIG40jdFBHjh7hYsJFdM06ahTVBEUNx878d/XLh5aBrRf4jzJM\nyBtkojCht1ckmrecmKR4mL1rFtPc3HzlIr8RkPgBnN8P/vGGCSp0On/1enzw4EHWrl1LSEgI4eHh\nALz++utkZ2cDMHfuXOLj49m+fTs+Pj6YmZmxevXqtv0mhFtO3759kcvlFBQU8OCDD9K7d2/2JC1B\nLUmUlgUQG9X5PlGYPXs2AwYMoF+/fnh4eODq4sq45yM44lYJNYVM7OvOk/9L5eilCiJ63Hj5k9D5\n3NCGedq0aZw7d47w8PCW0cWSJP3pBfq7775j+/btNDY2Ul1dzX333Se6a3RxAyYMYNHiRRibGuMW\ne8/Vo0ezD+t7F8e9A7JrjMm+xcR6DCCl9AgnT53hp59+ws7Ojoceeujygu79wchSX5YhNsxCK/g7\n1+OBAwf+6QmZJEl88MEHrZpV6DieffZZ4uLiuPPOO0lLS+Ptt99GkiQScvZiqdFypi6ahb2cDB2z\n1ZmZmZGWltbyZ2natGmEBDmwqm4HeZlbiQuewQubT7DxWK7YMHdxN7RhTk5OJiMj45o3gPyRN954\ngzfeeAOAffv28e6774rNchen0+n4dNWnoIYmdRMVaiUBLpZXLjq0DExsoPdUw4T8iwa43caS4++z\n5YPXANi/fz8ZGRmX+9sqjMBnqP7GP50O/sKfIUG4lr9zPRaE6ykpKWH58uUsWbKExsZGvLy8sLGx\nQafTcaD2EmHNSn42tSPMveO3k7sWrVaLQqHg6NGjODg48OyQp1m1dQdJF3ZzZ98HGRncja2pBbw4\nJggT5a1/kCO0jRuqYQ4ODqawsLCtswid3IgRIzj681GQ4Pa4sRj7RhPo8psLcMVFOL1VP9XPyNxQ\nMf+SXna9UGKJ29RoLC0tqa2t5Yknnrhykd9IqCmAwjTDhBQ6FXE9Flqbo6Mjw4YNo6GhAYVCQWho\nKJIkcbokjRJJg3WdKwN9HVDIb2jL0OGMGjWKHj160KNHD3bt2kVOaj5G2c0cqcwEYGIfd2qa1OzK\nKDJwUsGQbuiEubS0lMDAQPr164ex8eWC/+++++6G3mTw4MEMHjz4bwUUOgetVotCqaDopP6CI7ew\nQ6Y0ufKEOekTQIJ+sw0T8m+QSTJ6mIfTFJFC8jvF/GPqZDQazZWLfIYDkn6IiUuYQXIKncfNXo8F\n4bd+7bc8Z84cduzYgaurK4sWLQIg4dT/kHQ6CivDGBXb+eqXf+Xq6sqpU6fw9PTEx8eHKVOmYOUl\nI2mWDF1tCf17OuBqbcLGo7mMDbu6c4zQNdzQhvmll15q4xhCZyeTyahrrkMylvD29cYrZhzZJXI8\n7X85SW6qgWNrIGg8WLsZNuxf1K9bNFl1B1i7R1+zL0kSOp3u8kfmFo7g1ldfxxz7tGHDCh2euB4L\nrem9995j3bp19O/fH2dnZwC8vLwASCg4SHBTMymqMN7uRP2Xr6WoqIicnByMjY2Ji4sjfm4Y/ync\nSM6pb+keOZs7+7jx0b5zFFU34mz1520chc7nhj5fiY2NpUePHqhUKmJjY4mMjGwZsyoIN+L8+fNk\nnc1CbiGnuaaZUoUj/t0skf86MSplHTRVQ/TDhg36N4zvdTs6ncS+s3vRaDSo1eqrNzV+IyHvKNQW\nGySj0HmI67HQmtzd3amrq+Ojjz6iurqae++9F0mSKG8sJ72plNAmE1xc3HDq5JtECwsLLC0tUavV\n7NmzhwEhdwGQdH4HABP6uKPVwabjoidzV3VDG+ZPPvmEu+66izlz5gD6Earjx49v02BC55GZmYm3\ntzcVFRWoy9Qs/c9SThfVXu6/rNVC4kfg3g/c+xo27N/Qy8EFqaknxU4XWbhwIY6OjixatOjKISZ+\nv079222YkEKnIa7HQmuaMmVKS4cIjUbD00/rPwU7mJOADpBXd2dwr859ugz6DfPMmTMZPnw41dXV\nfL1iA/Xby0mqPAM6Hd6OFvTubsPGY6Inc1d1QxvmDz74gIMHD7aMUvX19aW4WJyUCTdGpVKhVCpp\nrNJvIE3tXKhpVF/eMGd9DxUXIHqeAVP+fZIk4SyPoEaby8ynZzJ58mSampqor//NONVuIWDpCpk7\nDBdU6BTE9VhoLfv370elUjF37lycnZ156623MDfXl8klnNuCvVrDxfqwTjUO+3oWL16MtbU1tra2\nlJSUULq3kkOSDl3RSUB/819mUS0n86sNnFQwhBvaMBsbG2NkdHm4hFqtFi2NhBtmbm6OjZ0NCnsF\n/eP6o7Z2ByDE7ZcOGYkfgpU7BIw1YMqb08c+Fp1Oxndnv2PLli2o1WqWLVt2eYEkQa+RcHYPqBoM\nF1To8MT1WGgNmZmZDB48mAkTJvDYY49hYWHBZ599BoBaq+ZgSQoxDQ1kKIPp62lr2LDtKDU1lYqK\nCj7//HM+3vYelcYKzmZsAGB0qAsKmcSWtHwDpxQM4YZrmF9//XUaGhrYvXs3kyZNYsyYMW2dTegE\nzp07x969e9HKtMiN5YwZOYbU3CqUcgl/F0soyoALCdDvQZDf8ODJW064qyeaWj82nf0Oj+4eALz7\n7rtUV//mJCJgDKjq4NxeA6UUOgNxPRZag7e3N5s3b+ann34C9D9Xv85OSC1JpUbbTGCDCX4+vig7\naTu5a3Fzc8PY2BiNRkNtlr5UJSlnHwA2ZkYM9HVgW1qBKMvogm7oT8Gbb76Jo6MjISEhfPzxx8TH\nx/Pqq6+2dTahE3jnnXeYOXMm5YXlNBc383/z/4/0vEr8u1lhrJDD0dUgN4befzylrCMIdLVCVRVB\nWWMJz3/6PPfccw9mZmacOHHi8qIeMWBiDae2GC6o0OGJ67HQGuRyOWPGjGnZ+A0fPpzY2FgA9ufs\nQ6HToarxIdav8033u5633nqL5557jsbGRg58f4Dsf59nb3E2NOtL7EaFuJBb0UBabpWBkwrt7YaO\n9GQyGePHj2f8+PE4OnaNWiahdVRUVKBUKlHpVDj76lsWpeVWMSbMFZrrIPVLfSs5c3sDJ705AS6W\nSPUBGEuW7CrYxfTp0/nyyy95/vnn2bNnj36RXAm94uHMdtCo9L8XhL9IXI+Fm7Vz505Onz6Nl5cX\nc+fOZceOHYSEhLQ8n3DpByIaG0lVB/J4F7jh77f69u1LcnIypqamODs7Y64040ijhPriARR+I7gj\nsBsL5elsTcsnzMPG0HGFdnTdE2adTsdLL72Eg4MD/v7+9OrVC0dHR15++eX2yid0cCNHjkSSSehU\nOiY8MIGLZfXUNKr1I1ZPbNS3kot4wNAxb5qxQo5/Nzss1FHszdlLRV0FAAkJCVcOMgkYA42VcPGA\ngZIKHZW4HgutZevWrSxZsoR//OMfrFq1ioyMDLZt2wZATk0O52pzia1vpMiuL242pgZO2/5cXV1p\naGjgnXfeoV90NNruZpw68y0A1mZKBvk6irKMLui6G+b333+fgwcPcuTIEcrKyigvL+fw4cMcPHiQ\nxYsXt1dGoYNaunQpycnJaDQaLMItmH7XdNJyKwEIcbOBIyvBKRA8ogyctHWEultTlh+GWqum1LUU\nSZLQaDSsXbv28iLvoaA0F2UZwl8mrsdCa1m2bBkbNmygoqKC+vp68vPzmTVrFgAJuQkA+NcZE+Af\nZMiYBhMVFYWJiQlmZmYYqU3RqrUcuHSo5flRoS7kVzVyPKfSgCmF9nbdDfOaNWtYv359y9QfgJ49\ne/LFF1+wZs2aNg8ndGzLli1j+fLlqFVqFEoFfTz6kJZbhbFChp8mCwpS9KfLneQO/zB3G2pqHQmz\nj2RTzibOnj9LVFTUlXXMSlPwHQ6ntoJW88cvJgi/I67HQmv49VTU1dUVSZKQJAlHR0dsbfWdMBJy\nEuih1pLT3IvYXs6GjGowTk5OHDx4kPr6eorzislakMm6n/Oh4iIAtwc6YySXsS2twLBBhXZ13Q2z\nSqXCwcHhqscdHR1RqVRtFkro+FQqFZWVlXh4eGDZ3ZK4x+JQyBSk51YR5GqF4thqUJpB6GRDR201\noR76NnmhVmMpbigmXZ1OWloaixYtIisr6/LCgDFQVwy5RwyUVOiIbuZ6/MADD+Dk5ERwcPA1n9+3\nbx/W1taEh4cTHh4uyjw6KY1GQ0REBO+//z533nknb7zxBr179+bUqVMA1KnqOFKUxODaWlJkQfTz\nsjNwYsMJDg7G2NiYEydO4BngRqmXBc2n9GUrViZKBvk5sj29AK1WlGV0FdfdMP+21+dfeU4QFAoF\nERERFBQW0FDVwED/gWi0Ok7kV9Gvm1xfvxxyl75rRCfh42iBqVJOXYUPPjY+fJ7xOUql/sa+9957\n7/JC3ztAbiTKMoS/5GauxzNmzGDnzp3XXRMTE0NKSgopKSm88MILfyujcGurqqrC29ub9evXk5SU\nRElJCZmZmZiY6MdeJ+YnotKqGdTQgLbHIIwUXaed3O8ZGRnh4+NDWVkZ2ScKUPpZkJq1qeX50aEu\nFFQ1cjynwoAphfZ03T8NqampWFlZXfXL0tKS9PT0675wY2Mj/fr1IywsjKCgIF588cVWDS7cupqb\nmwkICCApKQmVSoXLvS5EukZyrqSW+mYNI7X7QVXfKW72+y2FXEaImzXHcyqZHjSdrIosbr/zdgCS\nk5MvLzSxgp5D4NR3IG4aEW7QzVyPBw0ahJ1d1z0tFPTs7Oz4+uuvcXJyQqfTYWxsTF5eXkuZz/7c\n/VjqZDg2WBIaHGbgtIa3a9cuHB0dsbOzQ1OhYuPJk9Cobyc3LMAJI4WMraIso8u47oZZo9FQXV19\n1a+ampo//QjQ2NiYPXv2kJqaSkpKCjt37iQxMbFVwwu3ppKSErKzsyktLUWulGPjbUO4Y/gvfSt1\nBORvBNfe+l+dTFRPO07kVRHjMhwHUwccpjrwyCOPUFhYSEJCwuWFgWOhMhvyjxkurNCh3Mz1+EYc\nOnSIsLAw4uLiOHnyZCskFm4lzc3NlJSUUFFRwdChQ5EkCXNzc+Ry/XAOrU5LQm4C/esbOawNZrB/\n16xf/i0XFxdkMhlqlZq8RXms+rYCzv4AgKWJklg/R3aeKBRlGV1Em33eIkkSFhYWgL72TqVSifGt\nXYizszOenp4EzgpkQNgAlHIlx7IrGGR8DuPyMxAx09AR20T/nvZodZCWU8fUgKn8nP8zRrZG5Obm\nMmLEiMttiPxHgUwJJ74xbGBBAPr06cOlS5dITU1l/vz5jB8//g/XrlixgoiICCIiIigpKWnHlMLN\n2L17Ny4uLsTExPD6668zadIkvv/++5ZrUkZZBmWNZQypqybPJhJHS2MDJzY8SZIIDw+ntLSU+uJG\nbO51oe701pbn40O6UVDVSEqu6JbRFbRpgZJGoyE8PBwnJyeGDx9OVFTnaB8m/LGmpiY0Gg0FBQVU\nVVdRVFxEtEs0AEcvVjDHfD8YW0HwBAMnbRu9u9tiJJeReL6MSX6TMFWYckZ1BtCXKeXn5+sXmtqC\nz+1w8lvQag2YWBDAysqq5YAjPj4elUpFaWnpNdfOnj2b5ORkkpOTxeCUDiQgIICRI0dy8uRJlEol\nw4YNY/To0S0HWftz9yNDYmBDI9YBQw2c9tbxn//8B09PT9TNamrzGjmas18/eAoYFuCMUi6xI12U\nZXQFbbphlsvlpKSkkJubS1JS0pXttX4hTis6l02bNuHp6UlTUxMKUwX2d9jT37U/VfUqiovyiG5I\ngLB7wMjc0FHbhKmRnHAPGxLPl2FtbM1Y77HkeOXQK6AXSqXyykb3wROhOg9yDhsusCAAhYWFLT+b\nSUlJaLVa7O079vRN4Uo9e/Zk+fLlgP7/94ABA3jqqadant+fs59AjRGl6m5EhXXN/svX4ufnx4gR\nIwAwUip5dVc5ZOvLS61MlMT4OrI9vVAMMekC2uUWWBsbGwYPHnzNu7TFaUXnolarAfDy8iJ4XDAO\nFg742vhyLLuCifIDyHUq6PsPA6dsW9E97UjPq6KmUcXUgKlojbXc/frdyOVyevfuTWFhoX5hrzhQ\nmOo7hghCG5oyZQr9+/fnzJkzuLu7s3LlSpYvX96ygdqwYQPBwcGEhYWxYMECvvzyS1FC14mkp6eT\nlJTEnj17mD17Nm5ubri6urY8X1RXxKnyUwyuKiPVKIwgVysDpr31SJKEiYkJldsr+eGHKnJ++qrl\nubjgbuRVNpCeV2XAhEJ7aLMNc0lJCZWV+rqehoYGfvjhB/z9/dvq7YRbhLe3NzY2NpSXl1PrW0u0\nSzSSJJF8sYypih/RuEeBc6ChY7apaG99HXPi+XK8rL0Y5D6IfU37MDIyorS0lLlz5+oXGluA3wjI\n2AQatWFDC53a+vXrKSgoQKVSkZuby8yZM5k7d27Lz+IjjzzCyZMnSU1NJTExkdtuu83AiYXW9Npr\nr9G/f3+mT59OdXU1ubm5fPPN5fsnEvL0NyQPq6+BHoPEP5Z+Z+HChTQ3N1OVXY1ODRVZu1s6HA0P\ndEYhk9ieXmjglEJba7MNc0FBAUOGDCE0NJTIyEiGDx/O6NGj2+rthFvAd999x5NPPkl9fT29o3rT\nYNNAf9f+ADRk7sNLKkQe2blayV1LhKcdFsYK9pwuBuC+gPsobyzHppsNAOXl5ZcXB0+EuhK4mHCt\nlxIEQbhpzz33XEuJTXh4OJs3b+aee+5peT4hJwFHTPFqVtMrOt5QMW9Z3bt359ixYxiZGGHsbky2\ncaV+Ui1gY2bEAB8HtqcXiLKMTk7RVi8cGhrK8ePH2+rlhVvQtGnTqK6uBiBySiQ7pB30d+lPk1pD\nROkmGpSWmAaOM3DKtmekkBHj68De08XodDqiXaLpad2T2hm1lL1Whq+vLyqVSj/UxPcOMLLUl2V4\nixttBEFofSEhIfj5+VFSUsJXX33FsWOX21k2qBtILEhkcJ2WLJkXQd6eBkx666qoqECr1mJub86C\nz6rQqN9i3ItfAvpuGc9sTOdkfjXBbp1nGJdwpa47xkdodePG6TfDK1asIN8pn0D7QJzNnUk/ncXt\n0hGKvSeC0tTAKdvHUH8nCqsbySioRpIkJvpOpMiliHtn3suqVavo2bOn/jRCaQIBo/VT/9RNho4t\nCEIn88QTT/Dss88SGBjIXXfdRWRk5BXPJ+Yn0qhpZFx1PuXOt4lyjD/g5eWFm5sbVelVXLzUxNuf\nbUHzyz07wwO7IZdJ7DghumV0ZmLDLLSKX6dGSZLElu1bSCtJY7DHYADqkj7HSNLgEDvHsCHb0eBe\nTkgS7DmlL8sY4z0GpVyJeX99d5Dc3NzLN8EGT9RPjzr7o6HiCoLQCWk0GpYuXcq7777LunXrqK+v\np6LiylHOe3L2YCoZE9VYj334KAMlvfV5enry1ltvIZfL0angQnkD2cn6a7iduRH9e9qLbhmdnNgw\nCzetubkZFxcXPv30UwICArhj3h3o0DHYfTBotfjlfsMJZQjmbp37Zr/fcrQ0Jszdht2nigCwNbFl\nqMdQElWJmJubY29vj7u7u35xz8Fg5gCp6w2WVxCEzkcul7N48WLUajUKhYJ169bx+eeftzyv1qrZ\nl7OPwAZTVJjg23eYAdPe+u6++25ihsQgt5Tz7uOOKM9fPuSIC+nGhdI6zhTVGDCh0JbEhlm4aevW\nraOoqAilUsmmTZs4qzyLs5kz/nb+1J36ARdtIZe87vnzF+pkRgZ3Iy23ipzyegAm+k6kVltL7NhY\nevXqxbx58/SdZORKCJkEmTuhvvxPXlUQBOHGBQUF4e3tTVVVFXl5eZiaXi6LSylOobKpkhFVReTb\n9UOmFNP9rken03Eq9RSSVmLBihqi5i3j9KlTANwR2A2ZhOiW0YmJDbNw02bMmIGfnx86nQ5bR1t+\nzv+ZwR6DkSSJmoMrKNNZ4hw10dAx292oEBcAtv8yBSraNRoXcxc8/uFBVlYWBw8eZNq0afrF4VNA\n0yx6MguC0CqOHz+Ok5MT48aNIzo6Gmtr65Y++b/ak7MHOQrGNhRjHRJnoKQdhyRJvP322+iadZTl\nN4BWzeDYGOrq6nC0NKafl13L9V7ofMSGWbgpzc3NTJo0iaKiIoyMjDhZc5IGdYO+frkyB8f8PWxi\nCGE9nA0dtd152JkR5m7Ntl8uoDJJRrxXPIkFiQwYNACAnTt30tjYCN1CwSlIlGUIgtAqdu/eTUlJ\nCdXV1SgUCiZNmkRAQEDL8zqdjj3Ze3BvtMFcp8NR1C/fkPvvv5/wmHAAQrsr+c/s2JZT+1EhLpwt\nriVLlGV0SmLDLNwUf39/NmzYgJWVFRs3bmTXpV1YKi3p160f2sMrAB3Z3veilHfNH7X4EBfScqvI\nLtOXZcR5xaHRacABZDIZn332GfX19SBJEH4v5B2FkjMGTi0IQkf3yCOPIJfLkclkBAYG8sknn+hb\nWf4isyKTvNo8BlTXUWXuBbaindyNevb/nkVmKiOr0ZSGs4fIuXQJgBFB3ZBEWUan1TV3MUKr0Ol0\nWFpaolAomDBhArG3x/LDpR8Y3mM4RhoV2qOf870mgqje4YaOajDxv5Rl/HrK7Gfrh7e1N0TCK6+8\nwn333UdMTIz+zurQySDJIWWdISMLgtDB1dfXc/78ed577z2Cg4OvGIP9qz05ewCJ6Q0XMfG/o/1D\ndmC9XHqhbdRSUNHEjK8KWDBrGl9++SVOViZEeoqyjM5KbJiFv62yspJXX30VtVrN/v372Z+zn3p1\nPaO8RkHaVyiaq/hCF0esn6OhoxqMh50ZYR42LRdQSZKI84rjrOIsY+8dC0BGRgZfffUVWDiBz+2Q\n9hVoNYaMLQhCB9a3b19CQ0N58sknyczM5NChQ1et+fHSHqwaHXDVNmEcIDbMf0VwcDBT3ppCfVUT\npkrIvXCajRv195+MDnPhTFENpwqqDZxSaG1iwyz8LRkZGTg7OzNjxgwA5s+fz7bz23AydaKvUx90\nhz/mjOSFuW8M5sZtNlCyQxgd4kJ6XhWXyuoAfVkGQFJVEt26dQN+My47fArUFMD5fYaIKghCB6fR\naFCr1eh0OkxMTDh69CjPPvvsFWvya/M5U3Ga8BoJrdwYPAcYKG3HNSJyBGjB1NyE1wdq+XrtKgBG\nh7qikElsOp5n4IRCaxMbZuFvWbJkCSqVioqKCnbt2sWoiaP4Ke8n4rzikF9MQCo5zYqmEcSHuhg6\nqsHFheg3xb+WZXS36k6QfRA7Lu3AxcWFYcOG8dNPP+nvYPeLAxMbSPmvISMLgtBByeVyRowYgSRJ\neHp6EhgYeLnn+y/2ZO8B4B/NOUg9Y7vMBNbWNPG2iXjM9KC8spEXfqiiT3gItbW12JgqGNzLkc0p\n+Wi0YohJZyI2zMLf8uSTT9KrVy/s7OwoKipif+F+1Do1o3qOgsTl1Mht2aOMYWSQ2DC725oR7mHD\ntrTLdW1xXnGcrjjNyo0rAVi/fj1Dhw7Vj8oOvVs/Kruu1FCRBUHogJqbm/n00085efIk8+bNw8fH\nh7q6uqvWfZe1C0WTHRHNRUj+ojvG32FhZEHsmFgcAh1IyteScS4bT09Ptm3bxvjebhRWN5J4vszQ\nMYVWJDbMwl+2atUqEhISyM7OprGxEZ1Ox1dnvsLP1g9/rQKyvmeNaigjwzwxNZIbOu4tYVSICyfz\nq1vKMkb2GImERGJ1InZ2dgD8/PPP+sURD+h7Mh//wlBxhU7mgQcewMnJieDg4Gs+r9PpWLBgAT4+\nPoSGhnLs2LF2Tii0hk2bNjFr1iz279/PuXPnKCwsxMzM7Io1lY2VnK5MJaTeBB2S/lMt4W+J9Yql\nUdkIwD/7KRg78nZcXV25PcAZS2MF34qyjE6lzTbMOTk5DBkyhICAAIKCgliyZElbvZXQjhobG5k7\ndy6zZs0iMDCQqKgoAoYHkFmRyb3+9yL9vAS1zJjVzbczOcL9z1+wixgZhTvCcQAAIABJREFUrC/L\n2HFC327I2dyZvs592XFhB/Pnz0culxMZGUlFRQU4+YPnQDi6GrRaQ8YWOokZM2awc+fOP3x+x44d\nZGVlkZWVxYoVK5g3b147phNai0ajv1lYLpczfvx4Dh48iCRJV6zZcX4POrQ8oClF8ugHll2vR35r\niXGPQW4ux6OnC2/9rMJJV4ytrS0mSjlxId3YeaKQhmZxA3dn0WYbZoVCwaJFizh16hSJiYl88MEH\nZGRktNXbCe2ktrYWjUaDkZERhYWF7N69m3Wn12FlZEW8Q290qV+yXTEMh27uhHvYGDruLePXISY7\n0q8sy7hQdQF7f3seeOABampqiIyMpKGhASL+ARUX4fwew4UWOo1Bgwa1fJJxLZs3b+b+++9HkiSi\no6OprKykoEC0xupoAgMD6d27N/369WPWrFnIZFf/Fb/+5DYklQWxNWdBlGPcFD9bP/o82odxyybi\naKnk3fX7GDd2LJs2bWJ8bzdqm9TsPlVk6JhCK2mzDbOLiwt9+vQBwNLSkoCAAPLyxMcTHZ2DgwNv\nv/021tbWlJWVcfLiSfZk72Gi70RMj6xEp9Pyds0dzIrpedXJRlcXF+JCam4VuRX6ISbDPYcjl+Ts\nztnNE088wdmzZzl37hyPP/44BIwFc0c4ssrAqYWuIC8vDw8Pj5bfu7u7i+t1B7NmzRoGDhyITCYj\nMTGR9euvnhpa3VjDhbpjhKkdkAD8R7d7zs5EkiQGug3kaMVRxgy7DQCFtpHJkyfjawUu1iaiW0Yn\n0i41zBcvXuT48eNERUW1x9sJbeSLL74gNDSUHTt2UFxcTHx8PD9W/IhWp+VuzxGQvJqDJoPQWHVn\nTNjVjfK7urhfyzJ+mQJla2JLtEs0Oy7ou2X8OoUrJycHFEbQZzqc2Q7l5w2WWegadLqr7+b/o3/w\nrlixgoiICCIiIigpKWnraMINmj17NrW1tZw+fZrHH3+c4cOHX7VmxdFtIKmZqa0ExwCw9zZA0s5l\nWPdhZO/NZtWm/bhZy3ExbmDhwoU4OjowLtyN/ZkllNQ0GTqm0ArafMNcW1vLxIkTef/997Gysrrq\neXHx7Tg+/PBD0tPTSU1N5ZFHHuGNxW+w/vR6hnsOx+3kFlDV8UrlSGYO9MJIIe4n/T1Pe3OCXK3Y\nfuLyR90jvUaSV5vHpaZLrF+/HkmS8PDwICsrC/rNArkSDn1gwNRCV+Du7q7/h9ovcnNzrzkdDvQb\ns+TkZJKTk3F07LpDiW4lTU1NKBT6fvd3330377zzDs7OV9cmf3d2B3K1JYOK0yB4YnvH7JSiXaNx\nCHEg+u5o/nn3EHan5bPo3XdISEjgrr7uaLQ6NhzNNXRMoRW06a5GpVIxceJEpk6dyoQJE665Rlx8\nO46YmBi6detGRUUFlpaWbC3eSqOmkYcD/wGHl5Nm3p8CYy/u6dfd0FFvWfEhLhzPriS/sgGAod2H\nopQp2XFxB6NHj+bHH39k+fLlDBgwAJ2Fs35c9vH/Qp1oTyS0nbFjx7JmzRp0Oh2JiYlYW1vj4iJa\nQnYUvw4nmT59esswqd/LLCmhXJvGQLmj/i/+4Gv/nSz8NcZyY4aHDcfoTiMe/vf7DPaUqK2r58EH\nHyT94G76edmxPikbrejJ3OG12YZZp9Mxc+ZMAgIC9DWZQoeWnp7Ogw8+SElJCVqtlp4BPVl/ej2j\nvEbR8+w+aKjgpYoRTIv2xKKLT/a7nl/LMnb+0i3DysiKgW4D+f7C92h1Wp5//nlkMhklJSX6cdn9\n54O6AY58YsjYQgc3ZcoU+vfvz5kzZ3B3d2flypUsX76c5cuXAxAfH0/Pnj3x8fFh1qxZfPjhhwZO\nLNyon3/+maFDh/LCCy+QlJTEv//972uuW3xwE5JMzbTGYnDtI8oxWtEwz2GUNZTx7y/WUdBkzpgg\nC7RaLT/++CNTo7qTXV7Pz+fEoUdH12Y7m4MHD7J27VpCQkIIDw8H4PXXXyc+Pr6t3lJoIxcvXiQ0\nNBSlUom1tTVRUVEU+RahylQxN/B+WDWacxZ9OVHhz/IBPQwd95bW09EC/26W7DhRwAMDvQB9t4y9\nOXs5VnSMhx9+mOPHj9PQ0KBvEeXkD74jIGkF3LYAjMz+5B0E4WrXugHstyRJ4oMPROlPR/TYY4/R\n1NSEJEnExMRcNQYboEmt4WDBHkxMLYksPAl3vGaApJ1XjFsMRpIRH733EU0VKoJsNBQXFrB69Wr+\n77l/YWumZF3SJQb6Ohg6qnAT2uyEeeDAgeh0OtLS0khJSSElJUVsljuohIQEAMzMzAgODubhfz3M\n15lfc5ffXXQ/tQPqSlhYOZaJfd1wsjQxcNpbX3yIC8mXKiiq1je8j3WPxURuws6LO7n33ns5f/48\n48aN47nnnuPgwYMw8J9QXyZOmQVBuMrw4cORy+WsXbuWZ555hh49ely1ZnPqebQmpxmudECGJMox\nWpm50pwB7gPwf8qfooI8HrzNEV9HI+rr6/l++1Ym9nFn18kiimsaDR1VuAnizizhT02ePJno6Giq\nqqqoqqrii9IvsDG2YX7gDDi4hAs2/UnS+PJgTE9DR+0Q4kO6odPB9yf1ZRlmSjNiPWLZfWk3Kq0K\nMzMz7O3tuXTpEvHx8Wjc+4H3MPhpMTRWGzi9IAi3iq1bt7Js2TLeeOMNli5d+ofrPj26DUmmZmLZ\nWfAeClaii1FrG+Y5jBq7Gi6o8hl690MMdKpDkiTmz5/PmEAb1Fod6w5nGzqmcBPEhlm4ro0bNzJ7\n9mwKCwuRyWQ88fkTnCg/wRMRT2B9fB00VPB81ThuD3DG29HC0HE7BB8nS/ycLdiWdrlbxuieoylv\nLOen3J9ISUlh1Sp9/+Wamhr9yOyhz0NDBSSK2lJBEPTtJydMmEB1dTVbtmxBq9Ve80bNjPxqspsP\nYSVZ0Ls8D/pON0Dazm9Y92GYyE34aPtHdLtnMZvPqHhrRgw+Pj58uvgNhvRy5IvESzSpxeS/jkps\nmIXrmjFjBmvXriUoKIjHnnqM5RnLiXCOYIzLQPh5GTlOQzjY0J1Z4nT5L4kLdiHpYnnLR3QD3QZi\nb2LPt2e/JSYmhqSkJCIiIjAxMSE1NRXc+uiHDPy8DOrLDZxeEARD++STT1CpVFhbW3Pu3DkSEhIw\nNTW9at1niadRmGcSjxEyc0fwizNA2s7P0siS2z1vJ7E8ESNjE+aMimD7vkTy8/P4/PPPuTvMgdLa\nZrakigmaHZXYMAt/qK6ujsbGRkxMTNi+fTuptanUq+p5Pvp5pMQPoamKl2rGE+ZuTWQPW0PH7VBG\nhbroyzJ+6ZahkCkY6z2WA7kHKGssIzIykiNHjuDh4cGCBQv0N2QNfR5UdbDvDQOnFwTB0MLCwrj/\n/vt55ZVXOHPmDCYmV98/Ut2oYtu575FkauLzz0D4vfqhSEKbGO8zHpWdio/3f8yzby/nv3ca4WSp\npKamhgMbV+LnbMHKny5cc1CQcOsTG2bhmnQ6HUqlknnz5mFsbMzE+yeS55fH9KDpeMvN4dCHFLqP\n5McKRx4UY7D/Mj9nS3ycLNiWfvm0YbzPeNQ6NdvObwP0J0j19fXodDoef/xxGq28IPJBOPIpFKYb\nKrogCAb28ccfc9ddd3HhwgUeffRRPvroo2uu+/ZYHlrzZNxk5oQ3NuinhwptJrJbJG4Wbmw+v5lG\n+yA+PO3AnT46jIyMyMjIYIK/OacKqjl0XrSY64jEhlm4plWrVmFlZcU333yDRqMhzysPTzdP5oTN\ngb2vg6aZN5on42Zj2tJbWPhr4kNcSLpQ3jI2tadNT0IdQ/k261t0Oh3u7u4td7w3NzeTkZEBQxaC\nqS1sfxrEKYUgdDkHDx5k7ty5ACQnJzN79uxrDivR6XR8lnQchfl5xleVI/WKF72X25hMkjHOexyH\nCw4zZ/4c3th5iQuFZbg42rJr1y62fPAS9uZKPtp3ztBRhb9BbJiFqzQ0NPDQQw/R1NSEvb09dz19\nFzU9algYtRDTsgtwfC1VIdPZnG3CvVHdUcjFj9HfMSrEBa0Odv7SLQNggs8EzlWd41jxMeLi4jhw\n4AC7d+9m4MCBvP/++2iMrGDYi5D9M6R9bcD0giAYgpGREWZmZjg6OjJ79mwWLFhwzSm5h86Xkaf6\nCYDRlaUw4NH2jtoljfUZiw4dbsPd+OTj5ayd5s2kUEtsbW3Zvm0b/pVJHMgq5Xh2haGjCn+R2OkI\nVykrK8PFxYWoqCia1E38kPkDwz2HM8h9EOz+Fxhbsko2CYVMYlKEu6Hjdlh+zhZ4O5qz/TfdMuJ7\nxmNtbM0XGV+0PObv709ycjJr165l2LBh0HsauEfCzmegpsgQ0QVBMICCggJeeeUVpk6dym233UZU\nVBSBgYHXXLv20EWMbY/RVwXu3fpC9+j2DdtFuVm4Mdh9MAnaBO6Zfh/y6Fk8HVSIqqkBY2Nj/m/W\n3diYKVm656yhowp/kdgwC1fZsGEDvXv3Ji0tjfzyfLoN68bTkU/D2R/h7A+oBz7B2rQabg9wFoNK\nboIkSYwKceHwhbKWsgxThSmT/CaxJ2cPuTW5gP7/h1qtBuDAgQM0q9Uw7kNoroet/xSlGYLQBVRX\nVxMZGcmWLVvYsmUL58+fp7z82h1ziqob+eH8EVCWMq6yTJwut7OZITOpaqri27Pf8lZCLT2W1DLY\nzwYTExNeXPgMdwVYsOd0MSfyqgwdVfgLxIZZaNHU1ERsbCz//Oc/+e677xgzdQy2k2x5JPIRupk6\nwu4XwMaT783GUV7XzJSo7oaO3OHFh15dlnFPr3uQIWPd6XUAzJ8/n+PHjxMREYGtrS25ubng6Kfv\nmnFmG6T/z1DxBUFoJ59//jl5eXnI5XJ0Oh2enp4ttcy/tz4pG6V1IiY6HcMtfaCXmLLbnsKdwunj\n1IfPTn7GyazzONpa8aB3IWqVik2bNrH88bvRXUxmmThl7lDEhllosXv3bhISEpAkCa1WS6aUif8g\nf6b4T4HkVVB0Am5/if8eLcTd1pQYHwdDR+7wejlb0tPRnK2p+S2POZs7c0ePO/gm6xtqm2uRy+UE\nBwfz3nvvUVFRQXBwMCtWrEAX/RC494PtT0FN4XXeRRCEjqy4uJgxY8bwyiuvMHToUA4fPsyyZcuQ\ny+VXrVVptPz3SAZG1imMqanFYvjLIBN/1be3mSEzKawrZMxTY7hwOp3hPiZ8969xGBsbU1xURD8X\nGTtPFnKmsMbQUYUbJP4UCS3i4+NZsWIFkydPJmpYFI2hjTwU/hBG9eXw48vQczAXnO/g53NlTOnX\nHZlMtJK7WZIkMS7MjcMXysmtqG95fHrQdOpUdXxx6nIts7u7O1qtloaGBubMmcPBQ4kw/iNQN8KW\nR0VphiB0QuXl5YwePZrAwED+9a9/sXv3bjZu3Iinp+c11+/OKKJRsQeNpOVe6yDoObhd8wp6MW4x\n+Nr6siZrDWprFwrc4lnz1TcoFQr69u3LW0/MxtxIzn9+zDJ0VOEGiQ2zAMDhw4dxd3fnqaeeYvfu\n3aSfSMfb0ZvRPUfD98/pN2Xxi/gyOQe5TGJSX3GzX2uZ0McNgM0pl0+ZA+0DGeoxlM9Pfk5Vk77O\nzcvLi2+++QYTExNMTU2JiooCBx9914zMnXB8rUHyC4LQdmbOnMmRI0doaGjAxsaGO+64g/nz5//h\n+jWHzmNtd4B+DY343PFmOyYVfkuSJB4Jf4SL1Rf56vRXjF2awvr0JqJ7OXP8+HHCAnwIbUhlw+at\npOVWGjqucAPEhlkgKSmJ6OhoCgoKqKqq4plPnqHHKz14vP/jyC/shxMbYODjNNv0ZENyLrcHOOFk\nJW72ay0edmb087Jj49HcKyZAPdL7EepUdaw+sbrlsTvvvJOVK1cSEhLCnDlzyM7OpiF0OvSIgZ3P\nQvkFQ3wLwi1u586d9OrVCx8fH9588+pN1L59+7C2tiY8PJzw8HBefvllA6QUfq+hoYFFixbRr18/\nLC0teeyxx7j//vtRKpXXXH+2uIaK0i+pUqiZ6hID3ULaObHwW0M8hhDlEsVHqR/x8qK32fXsYHZN\n0jBl8l3I5XK+XfoitYe/5o3tp8T0vw6gzTbMDzzwAE5OTgQHB7fVWwitxNXVlVGjRnH77bez4NEF\nfK/5nnC3cIZ06w/bngS7njDwn+zOKKKsrpkp/cTNfq1tYh83zpfWkZJz+aTB19aXOK841p1eR2lD\nacvjfn5+JCUlsXr1ary9vXn2uef0pRmSDDbNA63GEN+CcIvSaDQ8/PDD7Nixg4yMDNavX68fgvM7\nMTExpKSkkJKSwgsvvGCApMJvFRcXExkZyWuvvUZ5eTlarZZHH32UqVOn/uHXfJ5wGmu7vbhqdMSO\neL8d0wrXIkkSz0Q+Q62qlmPmx4id8w40lNPLpJyqqiruu+8+3vz4vxw6X86BrNI/f0HBoNpswzxj\nxgx27tzZVi8vtJL6+noWL15McXExCQkJrF6zmsLKQh7r8xjSgXeh/BzEvwtKE9YnZeNmY0qM79VN\n8oWbEx/igrFCxjfH8q54/OHwh1FpVSw+urjlsYiICFasWNHy+2nTpoGNB8S9DdmH4Of/tFtu4daX\nlJSEj48PPXv2xMjIiHvuuYfNmzcbOpZwHfX19fTr14+MjAxWrVrF+fPnmTZtGjY2Nn/4NSU1TSgz\nX+aUqcT9PhOQm1i1Y2Lhj/ja+jLJbxL/y/wfp0zNWZ7ty+tr9HujY8eO8dlzD+BiIePZFZvRasUp\n862szTbMgwYNws7Orq1eXmgFBQUFODs7895775GcnMyrb72K5wJPYnrEEKmWwU+LIWwK+AzjYmkd\nP50t5Z5ID+TiZr9WZ2miZERQN7ak5dOounxC3N2qO/8I+gffnfuOI4VHWh6fNWsWU6dOxcfHh5qa\nGjQaDQ1+4yBgDOx5DQrTDfFtCLegvLw8PDw8Wn7v7u5OXl7eVesOHTpEWFgYcXFxnDx5sj0jCr+j\nVCq54447sLCwwMLCAh8fH6ZMmXLdr9m/7b9csDuNvWTEXQOea6ekwo2Y33s+diZ2LPxpISET5jPa\nV86WV++jrq6O06dPc2H5PH7+z3z+myD+3N3KDF7DvGLFCiIiIoiIiKCkpMTQcbqUX28kMTY2Zs6c\nOZjGmoIXLAidA5vmgmU3GKmvd/zyyC83+0V4/MmrCn/X3ZEeVNar2HGi4IrHZ4XOws3CjVcSX0Gl\nUV1+fNYsTp8+zZAhQ3B0dGRgTAzNd7wDprbwzRxQN7X3tyDcgq5VGylJV/6jt0+fPly6dInU1FTm\nz5/P+PHj//D1xDW7bZ05c4b+/fsTFBRETU0N8+fP5+TJkwwaNOgPv6a+5BKml14l2dSEWX0WYCw3\nbsfEwp+xNrbm37f9m7OVZ0nsVsq6f01htLSX2TOm6jsf1VQQMO4hPj5cfMWBiXBrMfiGefbs2SQn\nJ5OcnIyjo/iov71oNBry8/MJCQmhqamJXqG9WJOxhhE9RhB4/GsozYSxS8HUhma1lg1Hcxjq70Q3\na3GzX1u5zdueno7mrDl06YrHTRWmLIxayIWqCyxPW97y+KBBg3jwwQeRJImKigosLS2RLBxg3DIo\nPgl7Xm3vb0G4Bbm7u5OTk9Py+9zcXFxdXa9YY2VlhYWFBaBvL6lSqSgtvXZNpbhmt52MjAxiYmI4\nevQor732GgD9+/dHoVD88Rc111OzZjIf2xnjYuzM5IB72ymt8FfEuMcwyW8Sn5/8nCMh46ipqeHT\nD/9DU1MTPXr0QHXie7KSD7B463FDRxX+gME3zEL7O3ToEA4ODsybN4+ysjJmzpxJXVgdzZpmHrEO\nhcQPod9s8BkGwK6MQkprm7lX3OzXpiRJ4r4oT45nV141MnWQ+yDGeo/l0/RPW0ozJEnizTffxNvb\nGyMjI5YtW6Y/8fMbAX2mw89L4eJBQ3wrwi0kMjKSrKwsLly4QHNzM19++SVjx469Yk1hYWHLSXRS\nUhJarRZ7e3tDxO3SysrKaGxsRKlU4uDgQFxcHPHx15nSp9Oh2jSfrbJ8Lhgp+L/bFqKUX7uDhmB4\nT0Y8SXer7jydvoy63ncSblvLwOgIrKysqCwtgmP/Y+GkAaxev9HQUYVrEBvmLmj16tVUVuq7Mbz0\n0kv8+/1/s+HcBsZ3H06Pnf+CbqEw/JWW9WsPXcLDzpRYP3Ga1NYm9nXHVCln9cGLVz23MGohHpYe\nPHvg2ZbezPb29uzbt48ePXrQp08funfvTo8ePcgNehhsPfWlNY3V7fxdCLcShULBsmXLGDFiBAEB\nAUyePJmgoCCWL1/O8uX6Tyw2bNhAcHAwYWFhLFiwgC+//PKqsg2hbd199918/fXXgL4TzkcffcS2\nbduuOc2vxcEl5GduYqmNLRGOgxjafWg7pRX+DjOlGYsHL6ZOVceTpvV8PsmahMcCGDx4MIGBgVTl\nnQONim9OlBk6qnANbbZhnjJlCv379+fMmTO4u7uzcuXKtnor4QbpdDpOnDhB9+76k+JHHnmEBx54\ngCVHl6CQ5Mw9exS0apj0GSj1pReZRTUcvlDO1ChPMdmvHVibKrk70oPNKXnkVzZc8Zy50py3Br1F\nWWMZzyQ8g1qrBsDNzY3JkydjZGSEXC4nJyeHzEt5cOcKqMqF7581xLci3ELi4+PJzMzk3LlzPPec\n/oawuXPnMnfuXEB/LTh58iSpqakkJiZy2223GTJul7N06VI2bNjAp59+ikajr2EdMGDA9f/RkvY1\nzT+8yBwnTySZGW8NfrGd0go3w9fWl5cHvExq+SleD7wNXcYmNOUXSEhIYNiwoYyZ+U92fPACX+45\n2vKzINwa2mzDvH79egoKClCpVOTm5jJz5sy2eivhBqhUKmJjY+nduzcvvPACvXr14sknnySlOIUd\nF3cwXe5It9yjMO4DsPdu+br/Jl7CSCFjsrjZr93MGtQTgE8OnL/quSD7IP4V/S8O5h/k7SNv/397\ndx5XZZn/f/x19oXlsB5AVllcEMwNFxTB3DUt03Qmc6ZstVym1CarKZca08qvjdkv0ylFK03NNXIZ\ny63cMEwRNxQVUZAdDvs55/79wcjkiEedlHPA6/l48BA459y8P7f3/eHiPtd933Xfj4uLo7KyEkmS\nmDhxIt7e3qTkq6H7XyBlBZz8rsHyC4Jwe6qrq6mpqWHJkiVIkoRGo2HkyJG8+eabtuctn/kX0vpx\nvO4bQZamhlc7voVRb2y44MLvMiBkAE9HPc1aUzqf+gTyRtgpvL280Ol0aIozcfbwYfSgnvj6+pKT\nk2PvuMK/iSkZ94lz586xZ88ezGYzKpWKXbt2ERQUxPvJ7+Ol0DH29D5ImAZt/nN2fFmVmbW/ZDE4\n2g8PJ7Ud099f/N10PNzOn5UHM8kz3Xili0cjHuXPkX/m65NfsyJtBQD9+vXj9OnTjB07lkWLFtG2\nbVs6dOjA+79oau/2tXEClIrGKwiOoqamhoSEBKKjo7Farfj5+TFgwAAWLVrEH/7wh5u/MPMQfDOG\nxcbmbNVV0UIzlD9G2ZjnLDikiR0mMjRsKJ/oZWyWLpP55SRiYmJITj5El7atsFosVJprtxPBMYgB\n832gpKSEZcuWoVKpGDJkCKdPn8bHx4ekjCSO5h5lYnYW+tZDoeer173u218uYaoy80RXcbJfQ3up\nVxjVFiv/2HGm3sdf7vgyvYN6M+fQHNadWQdAaGgoc+fOpVmzZmi1tVNqEpd/CcP/CdVlsOFFELdf\nFQSHkZGRwenTpzlx4gTl5eUsXrwYtdrGwYlLybDiUb7y8GaBrgpVZTuWPiKmYjRGcpmc6bHTiQ+I\n510vDzakLmLMgM5kZWWxfeNqEh4fj+QXydBHH+PQoUMcOXLE3pHve2LA3ITl5eURGhqKm5sbs2fP\nJjo6mrfffpvg4GAKKguYs28WUVXVDPVsC8MWgfw/m4PFKrF4TwbtAt3oEORuxyruT6HezvyxcyBf\nHbhIRl7ZDY8r5Arm9pxLbLNYpu+bTtK5JADMZjM5OTlER0cDMHr0aP7y7v9jbnYPpDPb4eBnNyxL\nEISGYbVaef/99zl16hQffPBB3dVJXnnlFX766SdcXFxu/uLMg1gTH2G+hzuz9RI1pa356MH3cdGK\nd/8aK5VcxQfxHxDn25VZnm5sPDiV554Zi4uLC/5SHgbfIC6WSnTu3JmYmBjOnbtxmp7QcMSAuQmT\nyWScP38euVyOXC5nwIABdOzYEYC//2sSphoTs/BC8cdVoNJd99otqdlcLCjnhfhQcba8nUzq3QK1\nUs6736XVe/MJtULN/F7z6WDswLS90/j2zLd4eHiwZs0aNm/ezAsvvMC0adP4xz/+wV8XfstxXTfY\n+gZkHrRDNYIg5ObmMmfOHB588EH+/ve/4+TkxJNPPslrr71GZGTkzV94/ifKVgxjqrcH/9RKVBd2\nYWTgm8RF+DZceOGe0Cq1zO/7CUO9O7JQXYVrj3R2/7ybX1MO45KbSuHFU6i0OsaNG0dwcLC9497X\nxIC5iSkuLub1119n8uTJjB07FplMxmOPPcaxY8eYOXMmAFv2vsPW/COMq9ESPnojaF2vW4YkSXy6\n6yzNvZzoGykasr14u2h4uU8L/nXiKt8du1Lvc3RKHZ/0+YRuft14++e3WXZ8Gf3798doNPK3v/0N\njUZT12SXXgnnRIUn5q/HiPnMgtBAJElix44dSJKE0WjEaDRy5coV1Go106dP5/PPP8fDw+PmCzi+\njiOrRjLC15PtajDnDqadfixvDo5quCKEe0olVzFr4OeMc27F5ups3jg2kWnvT+NC+klc9Fpcej1P\n4pdfM3HiRLp06UJMTAxnz561d+z7jhgwNzFbtmxh9uzZzJs3j40bNxIZGcmSJUuIjIxEoVBwcs9s\n3jrzNW0lFU8+vgWcbrw5wdbjORzLKmZcfBgKcSk5u3qqewgPBBh4e8Nxckvrv9W1TqljwYML6Bfc\njw+SP2BBygIkSSIzMxOz2cxTTz1FSEgIiV+vpuP8C4T//TRlyx9yP1z2AAAdMElEQVSH6vIGrkYQ\n7j/r1q2jT58+zJo1i9atW3PixAkkSeLVV19lypQpN38HT5Io2fMhc3b8hT/7eFCtMyLPHo8vA1j0\nRCfUSvHruymRy+S8+MhX/FPyobIsl9nZswnpGkLnmGgqD6ykHA17fj5AcnIyly9frjtPRWg4Yo9r\nAqxWKykpKSQnJ2MwGFAoFDg5OdGyZUsmT56Mk5MTWGrI2zSeCacTcZGrmT9sHSonrxuWZbFKfLDt\nFGHeTjzawd8O1Qi/pVTImTviAcqqzbz45WGqzdZ6n6dSqJjbcy7DI4bz2dHPeH3v67Tv1J5jx47x\n1ltvsX37dqqqqvD1a8aFYnj+092YV4yCmsoGrkgQmj5JkuouBxYZGYler2fGjBmkp6fTq1cv1q9f\nz5QpU276+urKYr5ZPZwhZ/7JlwZXevoO5urJCeitYXz+ZAxuejFvuUlSqIgZtZq15Tr+XFaF9k8a\n8h7Lo/fzXbFWFJGaegwfv2a88847eHt78+WXX/Lwww8zd+7cWy9b+N3EgLkJmDx5Ml26dKFbt24M\nHDiQsLAwVq9ezYkTJ3jyySehKJOCZYN54cp2ilUaPh68Am9D/XOhVidnkn7VxJR+LVEqxObhCFr6\nujB3xAMcOl/I6+uOYbHWf6ULhVzB293eZkL7CWw+t5lntz2LX3M/oPZkwIqKCpycnJDL5aSU+eA/\n8TtGxIZRVSLuKiUId9O4cePo2LEjCxcuZMaMGWi1WuRyOfPnz+eHH37g4YcfrvcOfuU15SQe+j8G\nfh3HrIozBOt8eCpkPtv2xmN0MbBmXCzNvZzsUJHQYPQeGJ5Yy5QK2FhQxkOB3bnU6gLqZlZUXlpq\nAoMZO3YsAwcO5E9/+hNHjhzBaq09kCJJEllZWXYuoOkSI6JG7NKlS+zcuZOMjAxkMhlmsxmNRsOs\nWbMYOHBg7Vt9x9dzakkcT0iXOK/VM7/3J7T2alPv8vJMVby35SQxIe4MiBJzlx3J0AeaMal3BGsO\nX2LyN0dueqRZJpPxXNvnmBM3h9S8VEYnjeZ04WnCw8OZOXMmy5cvp6KignZd46mwqlmbfBl/Px++\nXvRhvScWCoJwe0wmE9XV1UBtb87NzWX8+PGsXLkSAIPBQOfOnet9bUFlAZ+kLKT/qgTeT/uc4Joa\n5oc9jZPlfT76vpJOIe6sfiGWZm66el8vNDHuIfBkEoEomXl4E9u7v89zf32O4Ef9MAzIRhPowg8/\n/IDVamXkyJEMHz6cEydOsHz5coKDg9m+fbu9K2iSbNxKSHBUFouFUaNGsX79eiwWC0qlktatWxMa\nGsratWtrj1xUFGHd+gZrzq5nrpcHBp0HS3p9RDtju5sud9bmNMqqzMx+NFpcGcMBvdy39qoZ7289\nxekcEx889gCRzVzrfe6g0EH4Ofvxys5XGP3daN7q9havvfZa3eNHjhyhrKr2gvhaJTz+whS++fIL\nPlm+EWNAcL1HvwRBqF9eXh4RERG4uLgwZcoUlEolRqMRSZJITEykR48eKJVK5PLrj1GdLz5PYloi\nG9M3UGWtJqGsnCc1QRwPmsmk7eVU1lzltYGteC4uFLk4n+T+4hUOTyXB8kfw/OoPzB/yEXPGzuGL\nI98yJ28OFxYfJWh0OPPmzWPVN6vIy82jqqqKKVOm0LNnTwBOnTqFv78/zs7Odi6maZBJDnRYqVOn\nTiQnJ9s7hsOyWCyMGDGCo0ePcu7cOeRyOWq1muHDh7Nw4UIMBgNIElLqWpJ3vMEHekjTqOni25k5\nPefiqbvxBL9rvknO5NU1R5nUO4KX+7ZowKqEO7XteDbTvj1Gflk1fSN9GNExgJ4R3ujUNw5yc8tz\neXX3qyTnJNMvuB+vd3kdT50nR48eZceOHYSGhhLTKoiAVh2QAGe1jAdaBvPliq8Ibtut4YtrxO7H\n/nU/1nyN2Wxm69athIeHA9CqVSvkcjkymQyLxYJarSY0NJRDhw5dN2CRJIkjuUdYmrqUHzN/RIWM\nIaYynjBVcdLreV7P7EhJpZU+rX14bWArwo1isHNfKy+A1X+GjN3wwOMw8D32pZ7j8cmTUA/VcXX9\nQYr2F+Osd8LH2we9Xs/ixYuZMGECOTk5BAYGsnfvXntX4ZDutH+JI8wO7toliZYuXcqWLVvIz6+d\nbzpy5EiSkpJ48cUXmTNnDgAV2Uf517bJfFl5gePuGnw0HrzX+VUGNh+IXHbz2Te/Zhbx5vpUuod7\nMuHB8AapS/jf9WvjS+fmHnzx03kS951ne1oOaoWcdkFuxIZ50i3Uk3ZBbmiUCrz13izut5ilx5fy\nyZFPOJh9kBfbvciINiNo27YtAJcvX0aj1VJZWYlFklF45QItO8Sy8tkoZP7tGTLmReQBnUAh2oUg\nXDNs2DA2b95MZGQkzZs3x9nZGZPJxNy5c2nXrh0xMTG4ubnVPb+8upr1p7ey6vQKzpWm4SSpGFtc\nxujiQg5YYxlTOZK8Ei8GRvnyp27BdAqxcak54f6h94An1sGu92DPPMjYRbf+75Kxcxc/nLrK39Tf\nkHz2NcxKM1Ut5Zz7PpXnnnueo0d/JTg4mKeeeorKykq+++47qqurGTZsmLjCxv9IHGF2UKmpqaxa\ntYp58+ZRXl6Oh4cHhYWFKJVKli1bxqhRo7h8+TK+zXw5nJ7E5sML2F55mTK5nBCVG0+0f5GhEY+g\nU9qe8/ZrZhFj/nkAF62KjeO74+msaaAKhbuhxmLlYEYBu0/n8vPZfFIvFyNJoFXJ6RTsQbcwT7qF\neRLtb+BCyTneOfAOh3MOE+gSyJjIMQwJHYKzuvYX/cWLF5EkibenTWHtpi11P+OZ9iomx3tSbmxH\nmx4PoWnZG7xbgpi2c537sX815ZolSaK0tBRX19ppTytWrGDmzJkMHjyYRx55hIcffpji4mJkMhmS\nJBEYGMiwYcN4Z/Ycjl028eulYjLyTKTnFpJRtZNqpx+Rqwtwr1HwXHE+j5pKOSh1YrXhz+gC2hIX\n4UVchDceTuIKGMJNXDoMmyZCTioEdYOeUzCH9GL59gN8sW8VWbKdXN1wDtNREz4demK+eoWiK+eJ\n7/8QP3y3DoANGzbQu3dvrly5gpOTE35+fvatyY7utH/d0wHzli1bmDRpEhaLhWeeeea6OZT1acrN\n1xZJkjh//jwfffQRS5cuxWQy4eLiQlFREQDu7u5MnToVFxcXsrKyeP3t1zmYvZ8fTq5id04yRVhw\nslrpqw/moc4vExPS2+YR5Ws2HMnijXWpuDup+OqZrgR66O91qcI9Vlxew4GMfPady2ff2XxOZpcC\n4KxREt/Sm/6RPmgNp/n8+CKO5x9Hp9TRM6An8QHxdPbtjFFv5PLly8TGxlJRUUH3LjGs35xUt3y1\nHA4+qyfAx8jbB3T06BnPyGdfQe4Vft8PoB25f92qF0uSxKRJk0hKSkKv17N06VI6dOhwy+U6cs13\nKjk5mXXr1jFjxgyUSiVTpkzhww8/ZO7cubi7uzN9+vS6KxCo1Wpqampo1aoVM2a9i0npSoHWnwMZ\nhRzJLKLaYkWmLMLNeAi5y09UyytpU23l6cJ8etYoqGw9Cm3sc2h8W9m5aqHRsVrgl0TYNQdKr4BP\nFHQdB62HkmeBN9a/x/K/fYTxYR+KdkqUnLiKVFMNMhlKjR6diysRbdrxy4+bQZJYvXo1gwYNYtu2\nbezfv593330XhUJBRUUFGo3mhnn3TYnDDJgtFgstWrRg+/btBAQEEBMTw9dff23z9p9Nqfn+N0mS\nqKmpYfHixeTk5KBQKNi6dSsHDhxAJpOhVCqpqqq9MYVMJiMyMpJhw4ZRVlbG1OlTOVeSTkrmblIu\n7+dX00WqsOJisRJfZaaXfxxx3aeh8wy7rSypWcXM/9cZ/nUih47B7nz8eHv8DOLs66Yo31TFgYwC\n9pzJZXtaDnmmatRKOXHhXkSHlZBt3cWBnD3kVeQB4Kn1pI1XG8LdwvF39sffyZ8xCWPIOJuBXC6n\nS8cH2H8ohWtNQ6uEweFyUq7CpRIY3qczjw0fzrmCGoJDI+jXrx/5+fk4OTlhNBrttyIagKP2r9vp\nxUlJSSxYsICkpCQOHDjApEmTOHDgwC2X7ag12yJJEmVlZaSnpzNx4kTi4uIIDAwkNTWVhQsXEh4e\njlKppKCggKtXryKTyVCr1VRVVREVFYV/QBBKV0+Mrbtg8uvAkYu1A2S5DKKayWjhfZh8635+qal9\nxya+vIKnSstpHxCHLPoxaDkQNGJesvA7mavh2Gr4eQHkngCFBlr0g1YPkWNsyWfnN7M+fT0Xv7pI\n3rZ8hs94me8/XEaFqRTJXA0KFVgtqFy90On0lOVfxmoxM+yxUbz516nMmzePTZs2sXPnTtq1a1c3\nD7pHjx52LvzucZgB8759+5g+fTpbt24FYPbs2QBMmzbtpq9pqOZbU1NDTU0NSqUSs9lMeXk51dXV\naDQaSkpKyM3NxWq14uzsTE5ODunp6Tg7O+Pu7k5qairp6emEhYXh4uLCxo0bKSgooFWrVmh1Gr79\n9lssZgs+ft6oNApSj5wCGahUSqxWK5b6LgcmA1cvLTHDglE5yfFvZ8AsWSmUarhMDZX/PnAnlyRa\nVtfQscZKgnskHaJHo2o5GNQ3XpfTbLFSabZiqjSTXVLJpcJyjmUVs+tULiezS3HRKhmXEMZzcaHi\nesv3CYtV4peLhWxJzWZLajZZRRUA+BnURASWoHO5RDnnuVp9lqsVmZgl839eW2XBReMC6ZDyYQpW\ns5VmrZrh6e7Mkd0n6p7n6QT5Zf/5maHeOi4VVIEMfDwNjBrci+Ubf8TLw4MBfXvRvkMnVq/bSGRk\na9o+0B4vbyMXMzOJjo5Gp9NhsVjqBnxWqxWTyYRcLsfb2xuFQkFlZSVWqxWNRoNCocBisVBdXY1K\npUKprN3nJEmqOxnrXnLUwePt9OLnn3+ehIQE/vjHPwLQsmVLdu7cecu3a+9FzRaLBbPZXHcUt6Cg\nAEmS8PHxIT8/n6NHjwLQq1cvUlJS+PHHH9FqtTz99NMsXbqUvXv34unpyfDhw3nnnXfIycnBzc2N\nZs2asWbNGtRqNSqVCplMRnFxMQqFApVKRWVlJQqFAkmS8PT0otRUSkSbdpw/c5J2Dw7FPSwaizGU\nwqIcXOSFOKny8Xcrw9upgHJlLueshZyS1WCRyfA2m3mkRslwn674txgMofGgc7+r60kQAJAkuHQI\nUtfC8XVgqr1hDoYg8vwi+UptZYPpEjmWUhQyOSVfFHH11zyGvDSSY3tOkbZnPwAyvStSeUndYmVK\nNZK5GoVKjVKhRKFUUG4qxdevGTq9Hjc3A5cyLxIVHYWERGiLUNLPphPaMpT8gnyCWgdRUFSAMdzI\n+ePn8W7hDUpQG9TkpOdgDDLi1cwLnU5HycUS3D3dCQoKQq/WU3KlBE83T3yNvuiUOsxlZtyc3XB3\ndker0KKQ352rODnMSX9ZWVkEBgbWfR0QEHBbRyzu1CuvvMLnn3+Or68vJ0+eZNy4cXz++edYLBY0\nGg2VlZXI5fK6a8xaLJa7ngHg0KFD131dVFQM1/5PZWCWWdCGabGUWJBr5TgHagkbYUSvBY1Mhop/\nf8jkVJnLUKGguVxJnMwJf5UzzV2CiDa2xymwa+1bMPWcgPXjyau89NUvVJmt9d7cQqWQ0S7QjbeH\nRPJohwAMOtW9WBWCg1LIZcSEeBAT4sGbg1tz/HIJBzMKSMksIuWigkuFWiAc6ANYkSlLkKsKkKkL\nUaqLKK0oQ+5rouuiQFydK8mvyCc/Kx+D2YDSoMSjlwemEyZkidnItDKU7kouqyWqc2v/SMzMKeT/\nVq/HUmolJ6+Q46fPYtQv4Wo5bPj3tA+jHq7+5o7d3nrI/e3X3t7k5ubi5OREWVkZXl5e5OXl4e/v\nT6tWrbh69SrHjh3j6aefZsmSJSQlJTFkyBBefPFFFi5cyNq1axkxYgRTp05l7ty5HDt2jC5durBo\n0SLGjBnD2bNn0el0NGvWrMH+X+612+nF9T0nKyvrnsxvXLVqFc8++ywpKSm8/PLLbNq0CblcTkZG\nBpGRkZSV1f7FdeXKFUJCQureebvVL7cJEyZc9/WCBQvqPtdoNHXLqaioQKPTU1JWgdK9GeaibOTu\nITh5B6HyDER9ZCUT2pYytbuOHOUpRgT4USpLplB2uHZhRrg2rDj9739drBKtZVrGOoeQ4N+TqIiH\nkHuKaUpCA5DJILBz7Uf/v8PVNLjwM1z4Ca+cNCYWZjDeauawVsNPOi0pj2tIfTKU4/LDyFtASNcQ\n8nfk49nXA5nSkyvfXKHyTCX6lipU7s6U/FpMVWk1cjcFCmcF2TmXwUrtXTys8OOOHwHYuWMnALu3\n7b7N3IAEChcFllJL3fKufa2P1FOZUYlnf09y1+fi1sONgGcCADj+7HF8B/sSMCIArNA2py1Lpiy5\n22v2BvdswFzfgev6jvB89tlnfPbZZwDk5ube8c/p1q0b58+fJzo6Gqg96pCamopMJiMsLIwTJ2qP\nfrm5uRESEsLevXvJy8vD2dmZ7t27c/ToUfLy8nB1dSUmJoatW7eiVCoJCAiga9eubNiwAZ1OR3Bw\nMF26deGzFZ/hpLfg6qKkRbSRjLQCPI3OaHUqWkf5oVGq8PEwoJdrCPL1wUVnwEljQK8xoNca0GoM\naDVuyNT62iPDKh0odXAX5gkFuOsY3SUIjVKBRilHo5KjUyvxc9Xia9AS4eOMRimuryvU7otR/gai\n/A1136ussZBVVMGlwgoKyqooq7JQXm3GVGWhxmLFapWwWCXa+LsyrH1t46o0V5I/Lp+CigJMNSbK\na8opf6OcspoyymrKqLZUk3UuC8lqxdVNRkluHr/+eJzSvBLaKIz0eqA5id/vI7+kFBedlqFdWzBv\n9U9YrBa8DXoe7hrBRxsPo9S54u7uzkMPPcTq1asJDQ3lwoUL9OrVi59//pnOnTvTpk0bioqKMJvN\n9O/fH4CwsDDi4+Pp3bs3AKGhoXTt2pXY2Figti+89NJLtGpVO5fUxcUFjaZpnfh6O734dvs1/P6e\nHR4eztNPP42rqyvx8fFkZGTQq1cvXFxc6NmzJ4cOHSIqKgpnZ2f69u1LSkoKnTt3pkOHDly4cAG1\nWk2XLl3Iy8vj3LlzuLq60rt3b06fPk1mZiZ+fn4MGjSItLQ0zGYzRqORTp064e3tTUxMDD/99BMm\ni4I0azNUCjlX0lNxcXWlWXAoaoWc8Kud8CtL44paTZVazlDzWZzVGjQKFSq5CrVKj07rhrdTM7wN\nQXh7tcHLEHhb540Iwj0lV4BvdO1Hl+drv2epQV50kZiyXGLKC6CiAEt5AVerC8msKqLQowxTbCUm\nSxXlzXtgHSHHYrVglaxYsVKYV0L2pXxcjO7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            "text/plain": [
              "<Figure size 1200x800 with 4 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plot_kdes()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "45bp131ngAxT"
      },
      "source": [
        "## Conclusion"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0xXnCEkKgDa5"
      },
      "source": [
        "In this Colab, we built VI surrogate posteriors using joint distributions and multipart bijectors, and fit them to estimate credible intervals for weights in a regression model on the radon dataset. For this simple model, more expressive surrogate posteriors performed similarly to a mean-field surrogate posterior. The tools we demonstrated, however, can be used to build a wide range of flexible surrogate posteriors suitable for more complex models. "
      ]
    }
  ],
  "metadata": {
    "colab": {
      "collapsed_sections": [],
      "name": "Variational_Inference_and_Joint_Distributions.ipynb",
      "toc_visible": true
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}
